Workshop on Bayesian Inference for Latent Gaussian Models ...gue20/masterfile.pdf · Welcome to the third workshop on Bayesian Inference for Latent Gaussian Models with Applications!

The Third Workshop onBayesian Inference for

Latent Gaussian Modelswith Applications

University of Iceland,September 12–14, 2013

Scientific Committee:

Veera BaladandayuthapaniAssociate Professor of StatisticsDepartment of BiostatisticsMD Anderson Cancer CenterUniversity of Texas

Birgir HrafnkelssonAssociate Professor of StatisticsDepartment of MathematicsFaculty of Physical SciencesSchool of Engineering and Natural SciencesUniversity of Iceland

Douglas NychkaDirector of Institute for Mathematics Applied to Geosciences Institute for Math-ematics Applied to GeosciencesNational Center for Atmospheric Research

Thomas Philip RunarssonProfessor of Industrial EngineeringDepartment of Industrial Engineering

Bayesian Inference for Latent Gaussian Models, September 12–14, 2013, Iceland

Faculty of Ind. Eng, - Mech. Eng, and Computer ScienceSchool of Engineering and Natural SciencesUniversity of Iceland

Daniel SimpsonResearcher in StatisticsDepartment of Mathematical SciencesNorwegian University of Science and Technology (NTNU)

Gunnar StefanssonProfessor of StatisticsDepartment of MathematicsFaculty of Physical SciencesSchool of Engineering and Natural SciencesUniversity of Iceland

Organising Committee:

Tinna Ýrr ArnardóttirIceland Travel

Ólafur Birgir DavíðssonUniversity of Iceland

Guðmundur EinarssonUniversity of Iceland

Óli Páll GeirssonUniversity of Iceland

Helga Lára GuðmundsdóttirIceland Travel

Birgir HrafnkelssonUniversity of Iceland

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Preface

Welcome to the third workshop on Bayesian Inference for Latent Gaussian Modelswith Applications!

Latent Gaussian models have already proven their value in various fields suchas climate, genetics, ecology, agriculture, medicine and biology, to name a fewand the spectrum of their applications is broadening. Thanks to faster meth-ods for inference and development of models for new applications, the fieldof latent Gaussian models continues to grow. This workshop brings togethermany of the researchers behind this growth. It sheds light on new findingsin the field and further work to be done. The emphasized topics of the work-shop are spatial and spatio-temporal modelling, Bayesian nonparametrics, machinelearning, and latent Gaussian models but other topics will also be covered suchas point processes and Bayesian computation.

The scientific programme contains two tutorials, talks of six invited speak-ers, seventeen talks in seven contributed sessions and a poster session witheighteen posters. Further information about these sessions can be found inthe abstracts contained in this book. There are also social events, along withsuggestions for other activities in the evenings.

We would like to thank Helga Lára Guðmundsdóttir and Tinna Ýrr Arnardót-tir at Iceland Travel for their work in organizing this event. We would alsolike to thank Atli Norðmann Sigurðarson, Helgi Sigurðarson, Ólafur BirgirDavíðsson and Óli Páll Geirsson for their contributions in organizing theworkshop. Our thanks go to the members of the scientific committee, VeeraBaladandayuthapani, Douglas Nychka, Thomas Philip Runarsson, Daniel Simp-son and Gunnar Stefansson, for putting together the workshop program. Fi-nally, we thank the Department of Applied Mathematics of the Science Insti-tute of the University of Iceland for funding this event, without its support,hosting this would not have been possible.

We sincerely hope that you will enjoy this workshop and your time in Iceland.

Birgir Hrafnkelsson and Guðmundur EinarssonReykjavík, September 2013

University of Iceland

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Contents

Preface 3

General Information 7Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Conference Badges . . . . . . . . . . . . . . . . . . . . . . . . . . 7Conference Rooms . . . . . . . . . . . . . . . . . . . . . . . . . . 7Preparation for Presentations . . . . . . . . . . . . . . . . . . . . 7Chairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Coffee & Lunches . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Reykjavík, Harpa and the University of Iceland . . . . . . . . . 8How to get there . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Venue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Internet Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Lunch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Programme at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Social Programme 13Social Gathering in Harpa . . . . . . . . . . . . . . . . . . . . . . . . . 13Poster Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Tour and Dinner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Scientific Programme 15Programme Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Thursday, 12th of September . . . . . . . . . . . . . . . . . . . . 16Friday, 13th of September . . . . . . . . . . . . . . . . . . . . . . 18Saturday, 14th of September . . . . . . . . . . . . . . . . . . . . . 20

Abstracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Invited Talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Contributed Presentations . . . . . . . . . . . . . . . . . . . . . . 33Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Participants 71

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General Information

Location

The Third Workshop on Bayesian Inference for Latent Gaussian Models withApplications will take place at Harpa conference hall.

Conference Badges

Your personal badge is your entrance ticket to the conference, coffee breaks &reception at Harpa Conference Center. Please remember always to wear yourbadge for easy identification.

Conference Rooms

All conference rooms are situated at Harpa Conference Center, 1st floor :Ríma ARíma BKaldalón

Preparation for Presentations

Speakers are asked to present themselves with their presentation material (ona USB memory key) in the same conference room as their presentation willbe held. Please do this during a break before your session starts.

Chairs

Please be present in the conference room at least 10 minutes before the begin-ning of the session.

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Coffee & Lunches

Coffee and refreshments will be served outside conference rooms Ríma A,Ríma B and Kaldalón.

Lunches are not included in the conference registration fee.

Reykjavík, Harpa and the University of Iceland

Reykjavík was first settled around 870 AD by Ingólfur Arnarson. It was notuntil the 18th century that any urban concentration started. The year 1786is regarded as the date of the city’s founding. Reykjavík is the northernmostcapital of a sovereign state, at 64◦08′. It’s mayor is Jón Gnarr, a well knowncomedian and actor. Reykjavík is the largest city in Iceland, holding a pop-ulation of approximately one hundred and twenty thousand people. Icelandis famous for it’s beautiful landscapes and geothermal energy and Reykjavíkcity is known for it’s 20th century style houses and entertaining night life.Iceland’s main source of income comes from fisheries. Other contributing ex-ports are aluminium, ferro-silicon alloys, machinery and electrical equipmentfor the fishing industry, software and woolen goods. The country has alsoestablished itself as a popular tourist destination. This year it is predictedthat around eight hundred thousand travellers will visit Iceland.

Harpa is a music and conference hall which opened in 2011. Harpa is theIcelandic word for harp. The building was designed by Studio Olafur Eliasson,Henning Larsen Architects and Batteríið Architects. In the spring of 2013, 1.8million people had already visited Harpa. Iceland has become widely knownfor it’s musical attires in which Harpa plays an important role. Many famousartists have performed at Harpa and it is a popular location to host music andart festivals. (From http://www.harpa.is)

The University of Iceland was founded in 1911 from three former post-secondaryinstitutions which taught theology, medicine and law. For the first yearthere were only 45 students and the University was situated in the houseof parliament for the first 29 years. In 1940 it moved to the University’smain building. Presently there are around 14 thousand students enrolledin the university in 25 faculties which span a wide spectrum of moderneducation. Most of the University’s houses are around Suðurgata. (Fromhttp://en.wikipedia.org/wiki/University_of_Iceland)

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http://www.harpa.is

http://en.wikipedia.org/wiki/University_of_Iceland

How to get there

How to get there

Most of the guests will be staying in hotels close to down-town Reykjavíkwhere it will only take 5-10 minutes to walk to Harpa. If you need to takea bus it is best to find a bus that stops at Lækjargata, since it is the closeststop to Harpa. You can find more information about the bus system at http://www.bus.is.

The map below shows Harpa and the surrounding area, Harpa is close to thetop labelled as National Music & Conference center. Lækjargata is the streetleading from the pond to Harpa. There are several restaurants on the streetsLaugarvegur and Austurstræti.

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http://www.bus.is

http://www.bus.is


Venue

The workshop takes place in three halls in Harpa:

• The tutorials will take place in the halls Ríma A and Ríma B, both on thefirst floor.

• The rest of the conference will take place in the bigger hall Kaldalón,also on the first floor.

Internet Access

The wireless internet access in Harpa is secured with the password Eldborg1,so one only has to find the desired network and connect. Many restaurantsoffer a free internet connection.

Lunch

There are many restaurants located in close vicinity to Harpa. There aresome inexpensive fast-food joints for example Bæjarins bestu which offers thefamous Icelandic hot dogs. Others are American style, Nonnabiti, Pizza king,Hamborgarabúllan, Beyglubarinn and Habibi. More expensive restaurants aresituated on Austurstræti and close to the harbour, feel free to ask the Icelandicattendees for suggestions and directions. There is also a restaurant locatedinside Harpa on the ground floor called MunnHarpan.

Programme at a Glance

The programme of the workshop is summarised in the following table. Detailsof the sessions are given in the Scientific Programme (page 15), and the dinnerand city tour are described in the Social Programme (page 13). This is a quickreference for the schedule to get an overview of the conference, the exacttimes can be found in the Scientific Programme.

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Lunch

Thursday 12.9.2013 Friday 13.9.2013 Saturday 14.9.2013(Ríma & Kaldalón) (Kaldalón) (Kaldalón)

08:0008:30

Registration

09:0009:30

Tutorials Invited 3:C. K. Wikle

Invited 5:J. Møller

10:00 Break Break Break

10:3011:0011:30

Tutorials Contributed 3 Contributed 6

11:4512:30

Lunch Lunch Lunch

13:00 Opening13:30 Inv. 1: M. Katzfuß

Invited 4:P. Müller

Invited 6:M. E. Khan

14:0014:30

Contributed 1 Contributed 4 Contributed 7

15:00 Break Break Break

15:3016:00

Invited 2:M. Sebag

Contributed 5

16:3017:0017:30

Contributed 2

18:00open end

Social gatheringin Harpa

Poster Sessionoutside thelecture halls

Conferencetour & dinner

Remember to look for the exact times in the Scientific Programme (page 15).Times might get shifted slightly because of the opening on thursday.At the tutorials the coffee break is from 10:30–10:45.

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Social Programme

Social Gathering in Harpa

At the end of the last session on Thursday there will be a social gathering inHarpa where people can enjoy a glass of wine and get to know each other.

Poster Session

The Poster session will be held outside the conference rooms Ríma A andRíma B on Friday at 16:30.

Tour and Dinner

The conference tour starts at 16:00 on Saturday.

Buses will be situated outside Harpa’s main entrance. Please make sure to beon time for the buses that leave at 16:00. We recommend wearing warm jack-ets for the tour or a windbreaker. Sandwiches will be served at the beginningof the conference tour.

The tour ends at Stokkseyri, which is a small town outside of Reykjavík. Therewe will enjoy a lovely dinner at Fjöruborðið, a respected restaurant. (http://www.fjorubordid.is/)

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http://www.fjorubordid.is/

http://www.fjorubordid.is/

Scientific Programme

Programme Overview

In the following, a more detailed overview of the scientific programme isprovided. There are six invited sessions, seven contributed sessions and oneposter session. The sessions approximate timings are included in the scheduleon page 11. For each presentation, authors, title and page number of theabstract are given. The name of the presenting author is underlined.

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Thursday, 12th of SeptemberVenue: Tutorials will be in halls Ríma A and Ríma B.The invited and contributed talks will be in Kaldalón.

Registration Thursday 08:00–09:00The registration will take place outside Kaldalón in Harpa.

Tutorial: Statistics for Spatio-Temporal Data Thur,09:00–10:30,10:45–11:45Lecturer: Christopher K. WikleHall: Ríma A

See page 24 for the course details.

Tutorial: Bayesian Nonparametrics Thursday 09:00–10:30, 10:45–11:45Lecturer: Peter MüllerHall: Ríma B

See page 25 for the course details.

Opening session Thursday 13:00–13:10Hilmar B. Janusson, Dean of school of Engineering and Natural Sciences, UI

Invited 1 Thursday 13:10–14:10Chair: Birgir Hrafnkelsson

• M. Katzfuß:Low-rank spatial models for large datasets (page 26)

Contributed 1 Thursday 14:20–15:10Chair: Birgir Hrafnkelsson

• A. Solin, J. Hartikainen & S. Särkkä:Time-Markovian representation of spatio-temporal Gaussian processes with ap-plications (page 60)

• J. Zammit-Mangion, J. Bamber & N. Schoen:Resolving the Antarctic contribution to sea-level rise: hierarchical modellingand source separation (page 66)

Invited 2 Thursday 15:40–16:40Chair: Thomas P. Runarsson

• M. Sebag:Robot training by modeling its teacher’s values and mistakes (page 31)

Contributed 2 Thursday 16:50–17:40

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Thursday, 12th of September

Chair: Thomas P. Runarsson

• L. Bornn:Towards the derandomization of Markov chain Monte Carlo for Bayesian in-ference (page 36)

• M. Girolami, H. Strathmann & D. Simpson:Exact Bayesian inference for large-scale GMRF models by playing Russianroulette without a gun (page 43)

Social gathering in Harpa Thursday 17:40–19:00Location: In front of Kaldalón

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Friday, 13th of SeptemberVenue: Kaldalón hall in Harpa.

Invited 3 Friday 09:00–10:00Chair: Douglas Nychka

• C. K. Wikle:Nonlinear dynamic spatio-temporal statistical models (page 32)

Contributed 3 Friday 10:30–11:45Chair: Douglas Nychka

• F. Lindgren:Boundary adjustment methods for SPDE models (page 52)

• F. . Bachl, A. Lenkoski, T. L. Thorarinsdottir & C. S Garbe:Spatio-temporal modeling and Bayesian inference on physical motion fields:estimating aerosol flow from satellite imagery (page 33)

• D. Bolin & J. Wallin:Spatial Matérn fields driven by non-Gaussian noise (page 35)

Invited 4 Friday 13:00–14:00Chair: Finn Lindgren

• P. Müller, J. Lee, Y. Zhu & Y. Ji:A nonparametric Bayesian model for local clustering (page 28)

Contributed 4 Friday 14:10–15:00Chair: Finn Lindgren

• V. Baladandayuthapani & J. S. Morris:Bayesian nonparametrics functional models for high-dimensional genomicsdata (page 34)

• G. Guillot:Analysis of spatial genetic variation with random field models (page 44)

Contributed 5 Friday 15:30–16:20Chair: Veera Baladandayuthapani

• M. Myllymäki , A. Särkkaä & A. Vehtari:Hierarchical second-order analysis of replicated spatial point patterns withnon-spatial covariates (page 55)

• K. Illner, C. Fuchs & F. J. Theis :Identification of biological processes combining blind source separation andlatent Gaussian models (page 49)

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Friday, 13th of September

Poster session in Harpa Friday 16:30–Open-endedLocation: In front of KaldalónSee page 21 for the list of posters.

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Saturday, 14th of SeptemberVenue: Kaldalón hall in Harpa.

Invited 5 Saturday 09:00–10:00Chair: Gunnar Stefánsson

• J. Møller , F. Lavancier & E. Rubak:Determinantal point processes and statistical inference (page 29)

Contributed 6 Saturday 10:30–11:45Chair: Gunnar Stefánsson

• D. Gamerman, T. R. dos Santos & G. C. Franco:A non-Gaussian family of state-space models with exact marginal likelihood(page 41)

• S. Muff, A. Riebler, H. Rue, P. Saner & L. Held:Measurement error in GLMMs with INLA (page 54)

• G. Fuglstad, D. Simpson, F. Lindgren & H. Rue:Non-stationary spatial modelling with application to spatial prediction of pre-cipitation (page 40)

Invited 6 Saturday 13:00–14:00Chair: Daniel Simpson

• M. E. Khan:Variational learning for non-conjugate latent Gaussian models (page 27)

Contributed 7 Saturday 14:10–15:25Chair: Daniel Simpson

• T. P. Runarsson & B. Hrafnkelsson:Recursive Bayesian inference for decision making using Monte Carlo rollouts(page 59)

• R. Jacobsen & J. Møller:Gaussian-log-Gaussian modelling of wavelets (page 51)

• T. G. Martins & H. Rue:Priors for flexibility parameters: the Student’s t case (page 53)

Conference tour and conference dinner Saturday 16:00–22:00 (approx.)Location: In front of KaldalónSee page 13 for further information.

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Saturday, 14th of September

Poster Session Friday starting 16:30

• B. Cseke, A. Zammit-Mangion, G. Sanguinetti & T. Heskes:Sparse approximate inference in spatio-temporal point-process models(page 37)

• Ó. B. Davíðsson, G. Einarsson & B. Hrafnkelsson:Bayesian hierarchical modeling of daily average temperature around Iceland(page 38)

• T. Doan, A. Parnell & J. Haslett:Reconstruct climate history at multiple locations given irregular observationsin time (page 39)

• Ó. P. Geirsson, D. Simpson, B. Hrafnkelsson & H. Sigurðarson:Modelling annual maximum 24 hour precipitation in Iceland using the SPDEapproach and a general block updating strategy for LGMs (page 42)

• D. Hammerling & J. Brynjarsdottir:Mesh settings for spatial analysis with INLA (page 45)

• Ø. Hoveid:Bayesian re-calibration of crop models with SPDE (page 46)

• B. Hrafnkelsson, V. Baladandayuthapani & J. S. Morris:Multilayer models based on two dimensional B-splines – an application to de-pendent extremes (page 47)

• J. B. Illian:Spatial modelling - challenges from ecology and criminology (page 48)

• R. Ingebrigtsen, F. Lindgren & I. Steinsland:Non-stationary spatial modelling of precipitation with the SPDE approach andR-INLA (page 50)

• C. J. Newby & J. R. Thompson:Subgroup discovery using a Dirichlet process mixture latent variable model ina clinical trial (page 56)

• A. Riebler & L. Held:Bayesian projections: Routine analysis without Markov chain Monte Carlo(page 57)

• L. Roinen:Discretisation schemes and convergence of Whittle-Matérn fields with an ap-plication in electrical impedance tomography (page 58)

• M. Shubin & J. Corander:Identifying Biological Events in the Bacterial Phenotypic Time-series (page 62)

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• H. Sigurdarson, Ó. P. Geirsson & B. Hrafnkelsson:Normal-normal models, linear constraints and relation to general LGM’s, withapplications. (page 61)

• A. Vehtari & H. Joensuu:A Gaussian processes model for survival analysis with time dependent covari-ates and interval censoring (page 63)

• E. Waldmann & T. Kneib:Bivariate Bayesian Quantile Regression (page 64)

• J. Wallin & J. Lindström:A temporal extension of non-Gaussian spatial Matérn fields (page 65)

• A. Zammit-Mangion, J. Rougier, N. Schön & J. Bamber:Resolving the Antarctic contribution to sea level rise: a hierarchical modellingapproach (page 67)

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Saturday, 14th of September

Abstracts

The following pages contain the abstracts for the tutorial (page 24), the in-vited talks (pages 26–32) and all contributed presentations (pages 33–67). Thenames of the respective presenting authors are underlined. The names of allauthors are collected in an index (page 68).

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Tutorial Short-Course: Statistics forSpatio-Temporal Data

Christopher K. Wikle

Department of Statistics, University of Missouri, [email protected]

This tutorial short-course presents the fundamentals of the statistical mod-eling of spatio-temporal data as described in detail in Statistics for Spatio-Temporal Data by Cressie and Wikle (Wiley, 2011). The course assumes basicbackground knowledge of spatial statistics and time series analysis. The fo-cus is on a basic presentation of exploratory methods for spatio-temporaldata, followed by a more in-depth description of spatio-temporal statisticalmethods in general, and hierarchical dynamical spatio-temporal models inparticular. Relevant examples will be included.

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mailto:[email protected]

Tutorial

Tutorial: Nonparametric Bayesian Inference

Peter Müller

Department of Mathematics, UT Austin , [email protected]

All models are wrong, but some are useful. Many statisticians know andappreciate G.E.P. Box’ comment on statistical modeling. Often the choice ofthe final inference model is a compromise of an accurate representation ofthe experimental conditions, a preference for parsimony and the need for apracticable implementation. The competing goals are not always honestlyspelled out, and the resulting uncertainties are not fully described. Over thelast 20 years a powerful inference approach that allows to mitigate some ofthese limitations has become increasingly popular. Bayesian nonparametric(BNP) inference allows to acknowledge uncertainy about an assumed sam-pling model while maintaining a practically feasible inference approach. Wecould take this feature as a pragmatic characterization of BNP as flexible priorprobability models that generalize traditional models by allowing for positiveprior probability for a very wide range of alternative models, while centeringthe prior around a parsimonious traditional model. A formal definition ofBNP is as probability models on infinite dimensional parameter spaces. Atypical application of BNP is to density estimation.

In this tutorial we review some of the popular models, including Dirichletprocess (DP) models, Polya tree models, DP mixtures and dependent DP(DDP) models. We will review some of the general modeling principles,including species sampling models, stick breaking priors, product partitionmodels for random partition and normalized random measures with indpen-dent increments. We will briefly discuss some of the main computationalalgorithms and available software.

Tentative table of contents:

1 Definition of BNP and introduction2 Density estimation Dirichlet process (DP); Stick breaking; DP mixtures;

DP clustering; DP mixtures: posterior simulation; Polya trees (PT)3 Regression BNP survival regression; Dependent DP (DDP); Anova DDP;

Weighted mixture of DP; Kernel stick breaking process; Gaussian pro-cess priors

4 Hierarchical priors Hierarchical DP; Nested DP5 Mixed effects models Random effects distributions; Multiple subpopu-

lations & classification

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Low-rank spatial models for large datasets

Matthias Katzfuss1

1 Department of Statistics, Texas A&M [email protected]

With the proliferation of modern high-resolution measuring instruments mountedon satellites, planes, ground-based vehicles and monitoring stations, a needhas arisen for statistical methods suitable for the analysis of large spatialdatasets observed on large, heterogeneous spatial domains.

Many statistical approaches to this problem rely on low-rank models, forwhich the process of interest is modeled as a linear combination of spatial ba-sis functions plus a fine-scale-variation term. I describe how low-rank modelscan be used for the analysis of global data, spatio-temporal data, distributeddata, and for data fusion.

The discussed methodology is illustrated using satellite CO2 measurements.

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Invited Talks

Variational learning for non-conjugate latentGaussian models

M. Emtiyaz Khan1

1 University of British Columbia, Vancouver, [email protected]

Bayesian learning in non-conjugate LGMs is difficult due to intractable inte-grals involving the Gaussian prior and non-conjugate likelihoods. Methods,such as MCMC algorithms, can potentially give accurate approximations butare slow and, many a times, difficult to tune. Variational Gaussian (VG)approximations are popular since they strike a favorable balance between ac-curacy, generality, speed, and ease of use. I will begin with a discussion ofmany real-world applications where VG approximations are shown to be use-ful. I will then discuss the two main problems of the variational approach:the computational inefficiency associated with the maximization of the lowerbound and the intractability of the lower bound. First problem can be partlysolved by establishing concavity of the lower bound and designing fast learn-ing algorithms using concave optimization. For the second problem, we canemploy tractable and accurate lower bounds, some of which have provableerror guarantees. Finally, I will show, through application to real-world data,that VG approximations not only make accurate learning possible, but canalso give rise to algorithms with a wide variety of speed-accuracy trade-offs.

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A nonparametric Bayesian model for localclustering

Peter Müller1, Juhee Lee

2 , Yitan Zhu3 & Yuan Ji 3

1 University of Texas, [email protected]

2 University of California Santa Cruz, [email protected]

3 NorthShore University HealthSystem, [email protected]

[email protected]

We propose a nonparametric Bayesian local clustering (NoB-LoC) approachfor heterogeneous data. The NoB-LoC model defines local clusters as blocksof a two-dimensional data matrix and produces inference about these clus-ters as a nested bidirectional clustering. Using protein expression data asan example, the NoB-LoC model clusters proteins (columns) into protein setsand simultaneously creates multiple partitions of samples (rows), one for eachprotein set. In other words, the sample partitions are nested within the proteinsets. Any pair of samples might belong to the same cluster for one protein setbut not for another. These local features are different from features obtainedby global clustering approaches such as hierarchical clustering, which createonly one partition of samples that applies for all proteins in the data set. As anadded and important feature, the NoB-LoC method probabilistically excludessets of irrelevant proteins and samples that do not meaningfully co-clusterwith other proteins and samples, thus improving the inference on the clus-tering of the remaining proteins and samples. Inference is guided by a jointprobability model for all random elements. We provide extensive examplesto demonstrate the unique features of the NoB-LoC model.

Keywords: Dirichlet process; Polya urn; Protein expression; RPPA; Randompartitions.

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Invited Talks

Determinantal Point Process Models andStatistical Inference

Jesper Møller1, Frédéric Lavancier

2 & Ege Rubak

1 Aalborg University, [email protected]

[email protected] University of Nantes, Nantes, [email protected]

Determinantal point processes (DPPs) are largely unexplored in statistics,though they possess a number of appealing properties and have been stud-ied in mathematical physics, combinatorics, and random matrix theory. Inthis talk we consider statistical models and inference for DPPs defined on Rd,with focus on d = 2.

DPPs are defined by a function C satisfying certain regularity conditions;usually C is a continuous covariance function where its spectrum is boundedby one. DPPs possess the following appealing properties:

a They are flexible models for repulsive interaction, except in cases withstrong repulsiveness (as e.g. in a hard-core point process).

b All orders of moments of a DPP are described by certain determinantsof matrices with entries given in terms of C.

c A DPP restricted to a compact set has a density (with respect to a Pois-son process) which is expressible in closed form.

d A DPP can easily be simulated, since it is a mixture of ‘determinantalprojection processes’.

e A one-to-one smooth transformation or an independent thinning of aDPP is also a DPP.

In contrast, Gibbs point processes, which constitute the usual class of modelsfor repulsive interaction, do not in general have moments that are express-ible in closed form, the density involves an intractable normalizing constant,rather time consuming Markov chain Monte Carlo methods are needed forsimulations and approximate likelihood inference, and an independent thin-ning of a Gibbs point process does not result in a tractable point process.

In the talk, we discuss the fundamental properties of DPPs, investigate howto construct parametric models, and study different inferential approaches

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based on moments or maximum likelihood.

Acknowledgement. Supported by the Danish Council for Independent Research— Natural Sciences, grant 09-072331, ”Point Process Modelling and Statisti-cal Inference”, and grant 12-124675, ”Mathematical and Statistical Analysisof Spatial Data”. Supported by the Centre for Stochastic Geometry and Ad-vanced Bioimaging, funded by a grant from the Villum Foundation.

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Invited Talks

Robot training by modeling its teacher’s valuesand mistakes

Michele Sebag1

1 Équipe A-O - Laboratoire de Recherche en Informatique, CNRS, [email protected]

Aimed at on-board robot training, an approach hybridizing active preferencelearning and reinforcement learning is presented: Interactive Bayesian PolicySearch (IBPS) builds a robotic controller through direct and frugal interac-tion with the human expert, who iteratively emits her preferences among afew behaviors demonstrated by the robot. These preferences allow the robotto gradually refine its policy utility estimate, and select a new policy to bedemonstrated after an Expected Utility of Selection criterion.

In order to cope with expert’s mistakes (or disinterest when demonstratedbehaviors are equally unsatisfactory), IBPS involves a noise model, enabling aresource-limited robot to soundly estimate the expert’s reliability and therebyenforcing a low sample complexity.

Interestingly, cumulative phenomenons are observed in the behavioral inter-action: when the robot prior is that the expert is competent, the robot learnsbetter – regardless of the actual expert’s consistency.

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Nonlinear dynamic spatio-temporal statisticalmodels

Christopher K. Wikle1

1 University of Missouri, [email protected]

Spatio-temporal statistical models are increasingly being used across a widevariety of scientific disciplines to describe and predict spatially explicit pro-cesses that evolve over time. Although descriptive models that approach thisproblem from the second-order (covariance) perspective are important, manyreal-world processes are dynamic, and it can be more efficient in such casesto characterize the associated spatio-temporal dependence by the use of dy-namic models. The challenge with the specification of such dynamical modelshas been related to the curse of dimensionality and the specification of real-istic dependence structures. Even in fairly simple linear/Gaussian settings,spatio-temporal statistical models are often over parameterized. Hierarchicalmodels have proven invaluable in their ability to deal to some extent withthis issue by allowing dependency among groups of parameters and science-based (e.g., PDE/IDE-model) parameterizations. The problems with lineardynamic models are compounded in the case of nonlinear models, yet theseare the processes that govern environmental and physical science. Here, wepresent some recent results for accommodating realistic nonlinear structurein hierarchical spatio-temporal models. In particular, we consider state-spacerepresentations using general quadratic nonlinearity structure. This perspec-tive represents a combination of scientific (mechanistic) knowledge, stochasticrepresentations of uncertainty and dependence, and observations in a latentGaussian framework. We discuss how the implementation of these modelscan be improved by the use of stochastic search variable selection, first-orderstatistical emulators, and time-frequency representations. These methodolo-gies will be presented and they will be illustrated with various environmentaland ecological applications.

32

Contributed Presentations

Spatio-temporal modeling and Bayesianinference on physical motion fields: estimatingaerosol flow from satellite imagery

Fabian E. Bachl1, Alex Lenkoski

2, Thordis L. Thorarinsdottir2 & Christoph

S. Garbe1

1 University of Heidelberg, [email protected]

[email protected] Norwegian Computing Center, [email protected]

[email protected]

Dust storms in the earth’s major desert regions significantly influence micro-physical weather processes, the CO2-cycle as well as the global climate ingeneral. Recent increases in the spatio-temporal resolution of remote sensinginstruments have created new opportunities to understand these phenomena.However, the scale of the data collected and the inherent stochasticity of theunderlying process poses significant challenges, requiring a careful combina-tion of image processing and statistical techniques. In particular, using satel-lite imagery data, we develop a statistical model of atmospheric transport thatrelies on a latent Gaussian Markov random field (GMRF) for inference. In do-ing so, we make a link between the optical flow method of Horn and Schunckand the formulation of the transport process as a latent field in a generalizedlinear model, which enables the use of INLA for inference. This frameworkis specified such that it satisfies the so-called integrated continuity equation,thereby intrinsically expressing the divergence of the field as a multiplicativefactor covering air compressibility and satellite column projection. The im-portance of this step – as well as treating the problem in a fully statisticalmanner – is emphasized by a simulation study where inference based on thislatent GMRF clearly reduces errors of the estimated flow field. We concludewith a study of the dynamics of dust storms formed over Africa and showthat our methodology is able to simultaneously infer the source of the stormplumes and accurately forecast the storm movement, two critical problems inthis field.

33


Bayesian nonparametric functional models forhigh-dimensional genomics data

Veera Baladandayuthapani1 & Jeffrey S Morris

1

1 University of Texas MD Anderson center, [email protected]

[email protected]

Due to rapid technological advances, various types of genomic, epigenomic,transcriptomic and proteomic data with different sizes, formats, and struc-tures have become available. These experiments typically yield data con-sisting of high-resolution genetic changes of hundreds/thousands of mark-ers across the whole chromosomal map. Modeling and inference in suchstudies is challenging, not only due to high dimensionality, but also dueto presence of structured dependencies (e.g. serial and spatial correlations).Using genome continuum models as a general principle we present a classof Bayesian methods to model these genomic profiles using functional dataanalysis approaches. Our methods allow for simultaneous characterization ofthese high-dimensional functions using non-parametric basis functions, jointmodeling of spatially correlated functional data and detection of local featuresin spatially heterogeneous functional data – to answer several important bio-logical questions. The models are parameterized as latent Gaussian processesthis allowing fast Bayesian computations. We illustrate our methodology byusing several real and simulated datasets and propose methods to integratevarious types of genomics data as well.

34


Spatial Matérn fields driven by non-Gaussiannoise

David Bolin1 & Jonas Wallin

2

1 Umeå University, [email protected]

2 Lund University, [email protected]

In this work, we study non-Gaussian extensions of a recently discovered linkbetween certain Gaussian random fields, expressed as solutions to stochasticpartial differential equations, and Gaussian Markov random fields. We showhow to construct efficient representations of non-Gaussian random fields drivenby generalized asymmetric Laplace noise and normal inverse Gaussian noise,and discuss how to do parameter estimation and spatial prediction for thesemodels. Finally, we look at an application to precipitation data from the USwhere we compare the results obtained using our non-Gaussian latent modelswith results obtained using standard Gaussian models for transformed data.

35


Towards the derandomization of Markov chainMonte Carlo for Bayesian inference

Luke Bornn1

1 Harvard [email protected]

In this paper, we explore the current trend towards conducting Bayesian infer-ence through Markov chain Monte Carlo (MCMC) algorithms which exhibitconverge at a rate faster than n−1/2 by derandomizing components of thealgorithm. For instance, herded Gibbs sampling (Bornn et al., 2013) can beshown to exhibit convergence in certain settings at a n−1 rate. These algo-rithms exhibit remarkable similarity to existing MCMC algorithms; as an ex-ample, herded Gibbs sampling is equivalent to the Wang-Landau algorithmwith various specified tuning parameters, and with the random samplingreplaced with an argmax step. We demonstrate that many such MCMC al-gorithms lie in a middle-ground between vanilla Gibbs samplers and deter-ministic algorithms by using clever auxiliary variable schemes to induce bothnegatively correlated samples as well as force exploration of the parameterspace. Based on this observation, we propose several new algorithms whichexploit elements of both MCMC and deterministic algorithms to improve ex-ploration and convergence.

36


Sparse approximate inference inspatio-temporal point-process models

Botond Cseke1, Andrew Zammit-Mangion

2 , Guido Sanguinetti1 & Tom Hes-

kes3

1 University of Edinburgh, United [email protected]

[email protected] University of Bristol, United [email protected]

3 Radboud University Nijmegen, The [email protected]

Analysis of spatio-temporal point patterns plays an important role in severaldisciplines, yet inference in these systems remains computationally challeng-ing due to the high resolution modelling generally required by large data setsand the analytically intractable likelihood function. Here, we exploit the spar-sity structure of a fully-discretised log-Gaussian Cox process model by usingexpectation constrained approximate inference. The resulting family of ex-pectation propagation algorithms scale well with the state dimension and thelength of the temporal horizon with moderate loss in distributional accuracy.They hence provide an flexible and faster alternative to both the filtering-smoothing type algorithms and the approaches which implement the Laplacemethod or expectation propagation on (block) sparse latent Gaussian mod-els. We demonstrate the use of the proposed method in the reconstruction ofconflict intensity levels in Afghanistan from a WikiLeaks data set.

Keywords: log Gaussian Cox process; time series analysis; finite elementmethods; variational approximate inference.

37


Bayesian hierarchical modeling of daily averagetemperature around Iceland

Olafur Birgir Davíðsson1, Guðmundur Einarsson

1 & Birgir Hrafnkels-son

1

1 University of Iceland, [email protected]

[email protected]

[email protected]

In this project a fully Bayesian hierarchical model is presented for daily aver-age temperature. The selected data-level distribution is a multivariate normaldue to its flexibility and theoretical basis in the field. The fit is assumed tobe governed by a long term fluctuation parameter vector, a periodic seasonaleffect parameter vector and a residual parameter vector that incorporates thetemporal correlation between calendar days. The covariance matrix of themultivariate normal distribution is assumed to be a diagonal matrix that con-tains only measurement errors. A periodic autoregressive (PAR) process isused to model the residual parameter and is fully incorporated into the iter-ative process used to estimate all parameters which is used since the modelparameters are correlated. The long term effect and periodic seasonal ef-fect are modeled as independent Gaussian processes governed by GaussianMarkov random fields.

A program in the R programming language is developed based on the modeland uses a Gibbs-sampler, a MCMC algorithm, to estimate all parametersthat are not assumed to be constant. The program is applied to observeddata stemming from four weather stations around Iceland. These locationsare Reykjavík, Dalartangi, Akureyri and Stórhöfði with measurements from1949 to 2010.

38


Reconstruct climate history at multiplelocations given irregular observations in time

Thinh Doan1, Andrew Parnell

2 & John Haslett1

1 Trinity College Dublin, [email protected]

[email protected] University College Dublin, [email protected]

The methodological focus in this poster concerns with multiple data seriesthat are irregularly observed, and misaligned. That is, the series yj = {yj(tij); j =1, ..., ni} have observations at different times. The application is to derive in-formation about the climate dynamic processes that generate climate variabil-ity in the past.

39


Non-stationary Spatial Modelling withApplications to Spatial Prediction ofPrecipitation

Geir-Arne Fuglstad1, Daniel Simpson

1 , Finn Lindgren2 & Håvard Rue

1

1 NTNU, [email protected]

[email protected] University of Bath, [email protected]

We introduce a non-stationary, spatial Gaussian random field (GRF) describedas the solution of a non-stationary stochastic partial differential equation(SPDE) and apply it to annual precipitation data for the conterminous US.The model allows a flexible covariance structure, which can be controlled bythe coefficients of the SPDE, and intuition about the global behaviour canbe gained from the local behaviour of the differential equation. Further, theformulation through an SPDE means that we can derive a Gaussian Markovrandom field with approximately the same distribution for use with compu-tations. The results show that the non-stationary model performs better thanthe stationary model for predictions.

40


A non-Gaussian family of state-space modelswith exact marginal likelihood

Dani Gamerman1, Thiago Rezende dos Santos

2

& Glaura C. Franco2

1 Universidade Federal do Rio de [email protected]

2 Universidade Federal de Minas Geraisglauraf,[email protected]

The Gaussian assumption generally employed in many state space models isusually not satisfied for real time series. Thus, in this work a broad familyof non-Gaussian models is defined by integrating and expanding previouswork in the literature. The expansion is obtained at two levels: at the obser-vational level it allows for many distributions not previously considered andat the latent state level it involves an expanded specification for the systemevolution. The class retains analytical availability of the marginal likelihoodfunction, uncommon outside Gaussianity. This expansion considerably in-creases the applicability of the models and solves many previously existingproblems such as long-term prediction, missing values and irregular tempo-ral spacing. Inference about the state components can be performed due tothe introduction of a new and exact smoothing procedure, in addition to fil-tered distributions. Inference for the hyperparameters is presented from theclassical and Bayesian perspectives. The results seem to indicate competi-tive results of the models when compared to other non-Gaussian state-spacemodels available. The methodology is applied to Gaussian and non-Gaussiandynamic linear models with time-varying means and variances and providesa computationally simple solution to inference in these models. The method-ology is illustrated in a number of examples.

Keywords: classical inference; Bayesian; forecasting; non-linear systemevolution; smoothing.

41


Modelling annual maximum 24 hourprecipitation in Iceland using the SPDEapproach and a general block updating strategyfor LGMs

Oli Pall Geirsson1, Birgir Hrafnkelsson

1 , Daniel Simpson2 & Helgi Sig-

urðarson1


[email protected]

[email protected] Norwegian University of Science and Technology, [email protected]

To obtain distributional properties of extreme precipitation on a high resolu-tion grid both observations and outputs from climate models are relied upon.A method for quantile predictions of extreme precipitation in Iceland is de-veloped combining these two sources. The method is based on observationsof annual maximum 24 hour precipitation from 86 observation stations inIceland and outputs from a local climate model on a 1 km regular grid. Acovariate based on the climate model is computed at each grid point and thenestimated with simple smoothing at each observation station.

A LGM is implemented for the observations, which are assumed to followthe generalized extreme value distribution. At the latent level, both locationand scale parameters are modelled with Matérn type spatial fields and thecovariate, allowing for spatial predictions on the high resolution grid. Inorder to make inference faster the Matérn fields are constructed with theSPDE approach on a triangulated grid over the domain of interest. An MCMCscheme is implemented for posterior inference, where a new general blockupdating strategy for LGMs is implemented to improve mixing.

Keywords: Latent Gaussian Models; Spatial extremes; Quantile predictions;MCMC block sampling.

42


Exact Bayesian inference for large-scale GMRFmodels by playing Russian roulette without agun

Mark Girolami1, Heiko Strathmann

1 & Daniel Simpson2

1 University College London, [email protected]

2 Norwegian University of Science and Technology, [email protected]

Exact Bayesian inference for large-scale GMRF models is oftentimes infeasibleto the complexity of computing related determinants of the fields covarianceoperator. We present a general scheme to exploit Exact-Approximate MCMCmethodology for intractable likelihoods by representing the intractable likeli-hood as an infinite Maclaurin or Geometric series expansion. Unbiased esti-mates of the likelihood can then be obtained by finite time stochastic trun-cations of the series via Russian Roulette sampling. Whilst the estimatesof the intractable likelihood are unbiased they induce a signed measure inthe exact-approximate MCMC procedure which may introduce bias in theinvariant distribution of the chain. By exploiting results from the QuantumChromodynamics literature the signed measures can be employed in an exact-approximate sampling scheme in such a way that expectations with respectto the desired target distribution are preserved. A large scale example will beprovided for a GMRF model, with fine scale mesh refinement, describing theOzone Column data, to our knowledge this is the first time that fully Bayesianinference over a model of this size has been feasible without the need to resortto any approximations.

43


Analysis of spatial genetic variation withrandom field models

Gilles Guillot1

1 Danmarks Tekniske Universitet, [email protected]

Genotypes of leaving organisms are routinely analyzed by ecologists and ge-neticists to understand and quantify the factors that affect genetic variation.The dramatic increase of dataset sizes enabled by recent sequencing tech-niques requires to use fast algorithms. We show here how geostatistical mod-els implemented within the INLA-SPDE approach can be used to addressquestions such as the quantification of gene flow or the detection of chromo-some regions under natural selection.

44


Mesh settings for spatial analysis with INLA

Dorit Hammerling1 & Jenny Brynjarsdottir

2

1 Duke University, [email protected]

2 Statistical and Applied Mathematical Sciences Institute, [email protected]

Integrated Nested Laplace Approximation (INLA) offers an efficient way toapproximate the posterior distribution in Bayesian analysis. The freely avail-able R package accompanying INLA makes it an attractive tool for routineBayesian data analysis. Combined with the Stochastic Partial DifferentialEquation (SPDE) approach INLA can be used to fit spatial and spatio-temporalstatistical models and to perform spatial predictions. The SPDE approach re-quires a definition of a mesh over the spatial domain, which can be conve-niently constructed using various helper functions in the R INLA package.The user has considerable control over the properties of the mesh throughparameters such as maximum edge length and minimum mesh angle. Thereis currently little guidelines on how to choose these parameters. With thegoal of providing more insight into sensible parameter choices we conduct asimulation study on the effect of different mesh parameter choices for point-reference observations of spatial fields with different characteristics of spatialdependence.

45


Bayesian re-calibration of crop models withSPDE

Øyvind Hoveid1

1 NILF, [email protected]

A changing climate will affect the conditions for crop growing and the prospectsfor food supply and security in the world. Partly will the climate be more orless favorable for crop yields depending on location, partly will increasingvariability of weather lead to increased variability of yields, partly will cropgrowing be moved from lands that become infertile into new lands.

The potential of crop growth is to large extent described with establishedgeneric models. Over the growing season are daily state variables with respectto soil and crop modeled as deterministic functions of previous day statesand current weather and management. These models are valuable sourcesof information on the stochastic production functions of crop growing. Theymight need re-calibration and addition of various errors, though, to obtainrealistic predictions of yields and management by weather and climate inactual production settings. Original calibration refers to observations fromexperiment stations, while predictions are needed for farms which do notconform with experiment protocols. The statistical task is to estimate cropmodel states, managements and parameters with Bayesian technique so thatobservations of farm yields and weather in space and time are accounted formodulo observation errors. In this context a non-linear day-by-day modelstructure is given. The statistical state variables are partly daily crop statesand weather, partly yearly and spatial crop model parameters. The hyper-parameters are related to the error structures of daily and yearly variables.Inference is sought primarily with respect to the yearly variables and theirspatio-temporal dependencies.

46


Multilayer models based on two dimensionalB-splines – an application to dependentextremes

Birgir Hrafnkelsson1 , Veera Baladandayuthapani

2 & Jeffrey S Mor-ris

2


2 University of Texas MD Anderson center, [email protected]

[email protected]

A particular type of multilayer models is presented. They are based on afinite number of layers plus a nugget effect. Each layer is defined on the samerectangle and modeled with two dimensional B-splines. The number of B-spline kernels increases by factor 4 from layer one to layer two, by factor 4from layer two to layer three and so on. A Markovian prior is used for theB-spline coefficients within each layer. The priors are independent betweenlayers and the correlation within a given layer for some pair of points on therectangle decreases from the first layer to the last layer.

These multilayer models are applied within a Bayesian hierarchical frame-work to data on annual maximum and minimum temperatures from Iceland.At the first level of the hierarchical framework the generalized extreme valuedistribution is used to model the data along with a Gaussian-copula. Themultilayer models are used at the second level in models for the location andscale parameters of the generalized extreme value distribution. The model ofthe location parameter also consists of a linear term based on altitude, dis-tance from open sea, latitude and longitude. These covariates are available ona fine grid and are utilized for spatial predictions.

Keywords: Multilayer models; Two dimensional B-splines; Markovian models.

47


Spatial modelling - challenges from ecology andcriminology

Janine B. Illian1

1 University of St [email protected]

Over the years, most of my research has involved interdisciplinary work ap-plying spatial statistics to problems in ecology. Using spatial statistics, andin particular point process methods, in ecology is a natural choice since alot ecological research is interested in the analysis of natural populations -large groups of individuals in space. Hence, spatial statistical methods havebeen used increasingly to tackle topical ecological questions. This talk willreview some of the contributions that this interdisciplinary work has made toecology, primarily in the context of biodiversity. Examples include assessingtheories of biodiversity, measuring biodiversity and modelling biodiversity inspace (and time). I will also discuss a number of more recent challenges I havecome across including several interesting applications from outside ecology,such as geolinguistics and crime modelling.

Keywords: spatial point processes; biodiversity; crime modelling;geolinguistics; INLA.

48


Identification of biological processes combiningblind source separation and latent Gaussiangraphical models

Katrin Illner1, Christiane Fuchs

1 & Fabian J. Theis1

1 Helmholtz Zentrum Munich, [email protected]

[email protected]

[email protected]

Many modern experimental techniques in biology result in large scale data,and often some prior information about the data-generating structure is given.In the field of gene regulation this might for example be measurements ofmRNA, miRNA and protein level together with a known underlying generegulatory network. The measured data, however, will typically be a mix-ture of different components that are associated to the network or to singlesubnetworks, respectively. We focus on this structural aspect and aim to sep-arate the mixture of observed signals into informative sources. Recently, weproposed a Gaussian graphical model with latent variables to describe thedependence structure of each source; to keep the parameter space small werequired wide sense stationarity within each source, and we estimated pa-rameters and sources using expectation maximization. The flexible Bayesianmodel allowed for including parameter priors and dealing with missing ormultiple observations of single variables. As an extension of our previouswork we now relax the stationarity assumptions and adapt the model to abroader range of regulatory systems, e.g. metabolomic fluxes. We demon-strate the separation performance on synthetic data and check for robustnessregarding network perturbations. Finally, we evaluate the model on gene ex-pression data and on metabolomic flux data. In both cases we first derive thedependence structure from the available network information. We demon-strate how the model identifies relevant biological processes and discuss howthe activity of given pathways can be determined using the model parameter.

49


Non-stationary spatial modelling ofprecipitation with the SPDE approach andR-INLA

Rikke Ingebrigtsen1, Finn Lindgren

2 & Ingelin Steinsland1

1 Department of Mathematical Science, Norwegian University of Science and Tech-nology (NTNU), Trondheim, [email protected]

[email protected] Department of Mathematical Sciences, University of Bath, Claverton Down, Bath,

United [email protected]

Geostatistical models have traditionally been stationary. However, physicalknowledge about underlying spatial processes often require models with non-stationary dependence structures. Thus, there has been an interest in the lit-erature to provide flexible models and computationally efficient methods fornon-stationary phenomena. In this work, we demonstrate that the stochas-tic partial differential equation approach (SPDE approach) to spatial mod-elling provides a flexible class of non-stationary models where explanatoryvariables easily can be included in the dependence structure. In addition,the SPDE approach enables computationally efficient Bayesian inference withintegrated nested Laplace approximations (INLA) available through the R-package R-INLA. We illustrate the suggested modelling frame-work with a case study of annual precipitation in southern Norway, and com-pare a non-stationary model with dependence structure governed by eleva-tion to a stationary model. Further, we use a simulation study to explore theannual precipitation models. We investigate identifiability of model param-eters and whether the deviance information criterion (DIC) is able to distin-guish datasets from the non-stationary and stationary models.

Keywords: Non-stationary covariance models; Gaussian random fields;Stochastic partial differential equations; Annual precipitation; ApproximateBayesian inference

50


Gaussian-log-Gaussian modelling of wavelets

Robert Jacobsen1 & Jesper Møller

1

1 Aalborg University, [email protected]

[email protected]

The coefficients in a wavelet transform and their dependencies are naturallyrepresented in graphical models known as tree structures. Here we proposea new model for such tree structures that also captures the non-Gaussiandistribution of the wavelet coefficients. The new model uses a latent Gaussianfield to model both the dependencies and variance structure of the waveletcoefficients.

Statistical inference in the model can be performed using both frequentist andBayesian methods, the latter in the form of INLA.

We demonstrate the model on real and simulated data.

51


Boundary adjustment methods for SPDEmodels

Finn Lindgren1

1 University of Bath, [email protected]

When using stochastic partial differential equation models to construct Markovrandom field models for spatial statistics, the issue of boundary effects needsto be considered. Sometimes, the underlying problem may dictate zero nor-mal derivatives along the boundary of a well-defined physical domain. Inother cases, the study area is only a part of a larger domain, and does notphysically end where the model ends. In such cases, more general bound-ary behaviour is desirable, for example in order to model a subregion of astationary random field, or to have different behaviour along sections of theboundary. Several methods for accomplishing this are presented, with vary-ing degrees of generality and practical applicability.

Keywords: Gaussian Markov random fields; Stochastic partial differentialequations; Boundary effects

52


Priors for flexibility parameters: the Student’s tcase

Thiago G. Martins1 & Håvard Rue

1

1 NTNU, [email protected]

[email protected]

We have extended INLA to fit a class of latent models, where components ofthe latent field can have near-Gaussian distributions, which we define to bedistributions that correct the Gaussian for skewness and/or kurtosis, allow-ing us extra modeling flexibility within the fast and accurate INLA frame-work. However, by leaving the realm of Gaussian distributions, the choice ofprior distributions for the hyperparameters that control higher moments ofsuch near-Gaussian distributions become even more challenging. We refer tothose hyperparameters as flexibility parameters. We present a novel approachto specify prior distributions for flexibility parameters that are based on thedistance between a basic model and a more complex model, where the com-plexity is controled by the flexibility parameters. We illustrate our approachon the interesting case of the Student’s t distribution, where the degrees offreedom parameter plays the role of flexibility parameter.

Keywords: latent models; INLA; prior distributions.

53


Measurement error in GLMMs with INLA

Stefanie Muff1, Andrea Riebler

2 , Håvard Rue2, Philippe Saner

1& Leon-hard Held

1

1 University of Zurich, [email protected]

[email protected]

[email protected] Norwegian University of Science and [email protected]

[email protected]

Important explanatory variables in applied sciences are often difficult to mea-sure and thus may contain considerable measurement error (ME). If such MEis ignored, parameter estimates and confidence intervals in statistical modelsoften suffer from serious biases. Bayesian inference of ME problems is usu-ally based on hierarchical models and has so far required the use of MCMCtechniques. Here, we show how Gaussian ME models fit into the frameworkof latent Gaussian models in the context of generalized linear mixed modelregression. We present an extension of the Integrated nested Laplace Approx-imations (INLA) approach to the classical and the Berkson ME models, whichare suitable for continuous error-prone covariates. Several examples illustratethe applicability of the new models.

54


Hierarchical second-order analysis of replicatedspatial point patterns with non-spatialcovariates

Mari Myllymäki1, Aila Särkkä

2 & Aki Vehtari3

1 Department of Biomedical Engineering and Computational Science, Aalto Uni-versity, [email protected]

2 Department of Mathematical Sciences, Chalmers University of Technology andUniversity of [email protected]

3 Department of Biomedical Engineering and Computational Science, Aalto Uni-versity, [email protected]

We suggest how to include the effect of non-spatial covariates into the spatialsecond-order analysis of replicated point patterns. The variance stabilizingtransformation of Ripley’s K function is used to summarize the spatial ar-rangement of points, and the relationship between this summary functionand covariates is modelled by hierarchical Gaussian process regression. Inparticular, we investigate how disease status and some other covariates af-fect the level and scale of clustering of epidermal nerve fibers. The data arepoint patterns with replicates extracted from skin blister samples taken from47 subjects.

55


Subgroup discovery using a Dirichlet processmixture latent variable model in a clinical trial

Dr Christopher J Newby1 & Prof John R Thompson

1

1 University of Leicester, [email protected]

[email protected]

Clinical trials are designed to determine the average effect of a drug, but stan-dard analyses do not provide information on how the drug affects individu-als. Some people may experience a large beneficial effect from the drug, whileothers show little to no effect or even an adverse effect. A Bayesian hierarchi-cal model is presented that uses a latent variable approach to analyse a setof clinical trial outcomes in order to search for subgroups of individuals withsimilar response patterns. The latent variables are modelled using a truncatedDirichlet Process Normal Mixture and are used to define the subgroups. Themodel is illustrated using a clinical trial of a new cancer drug that measuredtwo survival outcomes and a binary outcome. The analysis suggests the pres-ence of three mixtures in each treatment arm. Subgroups found in this waymay be important in the development of personalised medicine and the bettertargeting of treatments.

Keywords: Dirichlet Process Normal Mixture; Truncated Dirichlet Process;Clinical trial; Cancer drug

56


Bayesian projections: Routine analysis withoutMarkov chain Monte Carlo

Andrea Riebler1 & Leonhard Held

2

1 Department of Mathematical Sciences, NTNU, Trondheim, [email protected]

2 Division of Biostatistics, University of Zurich, [email protected]

The projection of cancer incidence and mortality data is of great importancefor the planning and organization of future health care measures. Although(Bayesian) age period cohort (APC) models are generally accepted for thispurpose, they are not used in routine practice of epidemiologists. Reasonsmight be, on one side, misunderstandings caused by the so called identifia-bility problem, but, on the other side, the lack of good standalone software. Inthis paper, we present a novel R-package built upon the recently proposed in-tegrated nested Laplace approximations (INLA) to generate projections basedon a Bayesian APC model. Due to deterministic approximations, time con-suming and difficult Markov chain Monte Carlo implementations become ob-solete. We illustrate how to obtain age-specific and age-standardised pre-dictions when age groups and periods are given for the same and differentinterval lengths. We conclude that Bayesian inference is now practically feasi-ble for age-period-cohort models, and hope that this stimulates a much wideruse of APC models among epidemiologists.

Keywords: Age-period-cohort model; Bayesian analysis; INLA; Projections;

57


Discretisation schemes and convergence ofWhittle-Matérn fields with an application inelectrical impedance tomography

Lassi Roininen1

1 Sodankylä Geophysical Observatory, [email protected]

We consider the discretisation scheme of certain Whittle-Matérn random fieldswith finite difference and finite element methods. We show that under suit-able discretisation scheme the discretised random fields converge to continu-ous random fields. The convergence study is based on two techniques: ma-joring techniques and the strong-weak convergence of probability measures.In Bayesian statistical inversion the study of the convergence of the prior dis-tributions is called discretisation-invariance. Discretised Whittle-Matérn ran-dom fields can be used as prior distributions in Bayesian statistical inverseproblems. By having the discretisation-invariant Whittle-Matérn priors, wecan show that also the posterior distributions converge in the discretisationlimit.

We apply the developed methods for an electrical impedance tomographyproblem, where the objective is to estimate the conductivity distribution in-side an object. Electric currents are injected into an object through the elec-trodes attached to the surface of the object. The problem is to estimate theconductivity distribution by measuring voltages induced by the injected cur-rents on the electrodes.

58


Bayesian Inference for Monte Carlo GamePlaying Strategies

Tómas Philip Rúnarsson1 & Birgir Hrafnkelsson

1

1 School of Engineering and Natural Sciences, University of [email protected]

[email protected]

The quality of a particular move or actions in games may be estimated by per-forming the move and observing the outcome of the game when both playersplay randomly. In the past this approach has been shown to be quite effec-tive, in selecting moves, for the game of Go. In this context, a Bernoulli trialis the outcome of such a Monte Carlo rollout. Similar approaches may be ap-plied to decision making problems where tasks are posed within the dynamicprogramming framework. The optimal allocation of Monte-Carlo trials is ofconsiderable interest, and a number of different strategies exist in the liter-ature for this purpose. For instance, the task may also be formulated as ann-armed bandit problem. The most popular, to date, approach to this prob-lem relies on estimating upper confidence bounds (UCB). Recently a Bayesianapproach to the UCB was proposed. We will study variations of this tech-nique by developing a Bayesian approach using the Beta distribution as theprior. An experimental study will be presented to illustrate the efficiency andeffectiveness of this approach.

59


Time-Markovian representation ofspatio-temporal Gaussian processes withapplications

Simo Särkkä1, Arno Solin

1 & Jouni Hartikainen1

1 Aalto university, [email protected]

[email protected] Rocsole [email protected]

Spatio-temporal Gaussian process models arise in many fields such as ma-chine learning, spatial statistics, physical inverse problems, and signal pro-cessing. A central practical problem in statistical inference on Gaussian pro-cesse models is the cubic O(N3) computational complexity in the number ofmeasurements N. In the spatio-temporal setting, when we obtain, say, Mmeasurements per time step and the total number of time steps is T, thistranslates into a cubic complexity in space and time O(M3T3). We discussone way to solve this problem, which is based on converting the covariancebased spatio-temporal model model into a time-Markovian stochastic partialdifferential equation (SPDE) model. Because of the Markovianity, we can useKalman filtering and smoothing methods which reduce the computationalcomplexity into linear in time O(M3T), and the spatial complexity M3 can befurther reduced close to linear by using sparse approximations.

We describe methods for converting spatio-temporal covariance function mod-els into time-Markovian stochastic partial differential equation (SPDE) mod-els. We also discuss the conversion of non-Markovian SPDEs, such as thecanonical Whittle SPDE, into time-Markovian form. We show how the time-Markov structure can be used for constructing Kalman filtering and smooth-ing based inference algorithms which scale linearly in the number of obser-vations, and show how the solution can be conveniently approximated withclassical Hilbert-space methods for PDEs. We apply the methodology to pre-diction of precipitation and to processing of fMRI brain imaging data.

60


Normal-normal models, linear constraints andrelation to general LGM’s, with applications.

Helgi Sigurðarson1, Oli Pall Geirsson

1 & Birgir Hrafnkelsson1

1 University of Iceland, [email protected],

[email protected]

In this work well known results about normal-normal models are reviewed.It is shown how results for linearly constrained normal-normal models canbe written in a form analogous to those for the unconstrained models. Fur-thermore, it is shown how many LGM’s with non-normal likelihoods can bewritten in a way that makes use of those results.

Applications are presented, with a focus on non-linear hydrological ratingcurves fitted into the class of normal-normal models and a brief look is takenat how spatial extreme value models fit into the more general LGM frame-work.

61


Identifying biological events in the bacterialphenotypic time-series

Mikhail Shubin1, Jukka Corander

1

1 University of Helsinki, [email protected]

[email protected]

BIOLOG Phenotype Microarrays (PMs) is a technology which allows screen-ing simultaneously the metabolic behaviour of bacteria in a large numberof conditions. PMs are applied in identification of the bacteria, drug devel-opment, cancer research and general biological studies. However, statisticalanalysis of experimental data usually does not exceed the basic toolbox andignores specific features of PMs. We propose a novel algorithm for decom-posing the PMs experimental data into components representing metaboliccycles of the bacteria, thus increasing the data’s potential for science.

62


A Gaussian processes model for survivalanalysis with time dependent covariates andinterval censoring

Aki Vehtari1& Heikki Joensuu

1

1 Aalto University, [email protected]

2 Department of Oncology, Helsinki University Central Hospital, Helsinki, [email protected]

We present a Gaussian processes model for nonhomogoneus Poisson pro-cess survival analysis with interval censored data. The benefit of Gaussianprocess model is that time dependent and baseline covariates may have fullinteractions. An example application is the estimation of the hazard of tu-mour recurrence in the follow-up for patients treated with adjuvant imatinibfor gastrointestinal stromal tumour. Shape of the individual hazard functiondepends on the surgery time covariates and time dependent covariates. Pre-dicted hazard functions for new patients can be used to optimize timing ofcomputed tomography examinations to reduce the time from recurrence toobservation without increasing the radiation dose and imaging costs.

63


Bivariate Bayesian quantile regression

Elisabeth Waldmann1& Thomas Kneib

1

1 University of Goettingen, [email protected]

[email protected]

Quantile regression for conditional random variables has become a widelyused tool to analyse relations within data. It provides detailed descriptionof the conditional distribution, without assuming a distribution type for theconditional distribution. The Bayesian version, which can be implemented byconsidering the asymmetric Laplace distribution (ALD) as an error distribu-tion is an attractive alternative to other methods, because it returns knowl-edge on the whole parameter distribution instead of solely point estimations.While for the univariate case there has been a lot of development in the lastfew years, multivariate responses have only been treated to little extent in theliterature, especially in the Bayesian case. By using a multivariate version ofthe location scale mixture representation for the ALD we are able to applyinference techniques developed for multivariate Gaussian models on multi-variate quantile regression and make thus the impact of covariates on thequantiles of more than one dependent variables feasible. This concept will beillustrated by an example on biodiversity data: the impact of different covari-ates like temperature, precipitation and habitat diversity on the number ofanimal and plant species will be explored simultaneously. A special interestlies in the differences of the conditional empirical correlations for differentquantile combinations.

64


A temporal extension of non-Gaussian spatialMatérn fields

Jonas Wallin1 & Johan Lindström

1

1 Lund University, [email protected]

[email protected]

In this work we let the error terms of an AR process be a non-Gaussian ran-dom field driven by generalized asymmetric Laplace noise. As opposed tothe Gaussian case, the casual nature of temporal models exhibits in the ob-served properties of the evolving fields. For example, the models are not timereversible. We are able to estimate the parameters using a Monte Carlo EMalgorithm. Finally the model is fitted to precipitation data from the AfricanSahel over several years, where the measurements have both areal and pointsupport.

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Resolving the Antarctic contribution to sea-levelrise: hierarchical modelling and sourceseparation.

Andrew Zammit-Mangion1, Nana Schoen

1 , Jonathan Bamber1 & Jonathan Rougier

1

1 University of Bristol, [email protected]

[email protected]

[email protected]

[email protected]

Determining the Antarctic contribution to sea-level rise from observationaldata is a complex problem. The number of physical processes involved (suchas ice dynamics and surface climate) exceeds the number of observables, someof which have very poor spatial definition. This has led, in general, to solu-tions that utilise strong prior assumptions or physically-based deterministicmodels to restrict the solution space. Here, we present a new approach forestimating the Antarctic contribution which only incorporates descriptive as-pects of the physically-based models in the analysis. In particular we useSPDEs and their relation to geo-statistical fields to incorporate physical un-derstanding (e.g. heterogeneous length scales) into the prior specification.Correlations between a subset of the physical mechanisms lead to a multivari-ate spatial process which may be approximated using GMRFs as in Lindgrenet al. (2011). The procedure allows, for the first time, a statistical evaluationof all latent processes affecting the Antarctic ice sheet with estimated sea-levelrise corroborating those found using a statistically independent method. On-going (i) computational issues stemming from a change of support problem(satellite geodesy) resulting in dense Cholesky factors and (ii) identifiabilityconcerns due to the under-determined nature of the source separation prob-lem (the "cocktail party problem") are discussed.

Keywords: SPDEs, GMRFs, source separation, physical-statisticalmodelling, sea-level rise

66


Resolving the Antarctic contribution to sea levelrise: a hierarchical modelling approach

Andrew Zammit-Mangion1, Nana Schoen

1 , Jonathan Bamber1 & Jonathan Rougier

1

1 University of Bristol, [email protected]

[email protected]

[email protected]

[email protected]

Determining the Antarctic contribution to sea-level rise from observationaldata is a complex problem. The number of physical processes involved (suchas ice dynamics and surface climate) exceeds the number of observables, someof which have very poor spatial definition. This has led, in general, to solu-tions that utilise strong prior assumptions or physically-based deterministicmodels to restrict the solution space. Here, we present new approaches (aspatial and a spatio-temporal approach) for estimating the Antarctic contri-bution which only incorporates descriptive aspects of the physically-basedmodels in the analysis. In particular we use SPDEs and their relation to geo-statistical fields to incorporate physical understanding (e.g. heterogeneouslength scales) into the prior specification. Correlations between a subset ofthe physical mechanisms lead to a multivariate spatial process which may beapproximated using GMRFs as in Lindgren et al. (2011). The procedure al-lows, for the first time, a statistical evaluation of all latent processes affectingthe Antarctic ice sheet with estimated sea-level rise corroborating those foundusing a statistically independent method.

Keywords: SPDEs, GMRFs, source separation, physical-statisticalmodelling, sea-level rise

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Author IndexBachl Fabian E., 33Baladandayuthapani Veera, 34, 47Bamber Jonathan, 66, 67Bolin David, 35Bornn Luke, 36Brynjarsdottir Jenny, 45

Corander Jukka, 62Cseke Botond, 37

Davíðsson Olafur Birgir, 38Doan Thinh, 39dos Santos Thiago Rezende, 41

Einarsson Guðmundur, 38

Franco Glaura C., 41Fuchs Christiane, 49Fuglstad Geir-Arne, 40

Gamerman Dani, 41Garbe Christoph S., 33Geirsson Oli Pall, 42, 61Girolami Mark, 43Guillot Gilles, 44

Hammerling Dorit, 45Hartikainen Jouni, 60Haslett John, 39Held Leonhard, 54, 57Heskes Tom, 37Hrafnkelsson Birgir, 38, 42, 47, 59, 61

Illner Katrin, 49Ingebrigtsen Rikke, 50

Jacobsen Robert, 51Ji Yuan, 28Joensuu Heikki, 63

K. Wikle Christopher, 24

Katzfuss Matthias, 26Khan M. Emtiyaz, 27Kneib Thomas, 64

Lavancier Frédéric, 29Lee Juhee, 28Lenkoski Alex, 33Lindgren Finn, 40, 50, 52Lindström Johan, 65

Müller Peter, 28Møller Jesper, 51Martins Thiago G., 53Morris Jeffrey S, 34, 47Muff Stefanie, 54Myllymäki Mari, 55Müller Peter, 25Møller Jesper, 29

Newby Dr Christopher J, 56

Parnell Andrew, 39

Rúnarsson Tómas Philip, 59Riebler Andrea, 54, 57Rougier Jonathan, 66, 67Rubak Ege, 29Rue Håvard, 40, 53, 54

Särkkä Aila, 55Särkkä Simo, 60Saner Philippe, 54Sanguinetti Guido, 37Schoen Nana, 66, 67Sebag Michele, 31Shubin Mikhail, 62Sigurðarson Helgi, 42, 61Simpson Daniel, 40, 42, 43Solin Arno, 60Steinsland Ingelin, 50

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Author Index

Strathmann Heiko, 43

Theis Fabian J., 49Thompson Prof John R, 56Thorarinsdottir Thordis L., 33

Vehtari Aki, 55, 63

Waldmann Elisabeth, 64Wallin Jonas, 35, 65Wikle Christopher K., 32

Zammit-Mangion Andrew, 37, 66, 67Zhu Yitan, 28

69

Participants

• Aðalgeirsdóttir, Guðfinna Th. [email protected]

University of Iceland• Bachl , Fabian [email protected]

University Heidelberg• Bakka , Haakon [email protected]

Norwegian University of Science and Technology• Baladandayuthapani , Veera [email protected]

University of Texas, MD Anderson Cancer Center• Bolin , David [email protected]

Umeå University• Bornn , Luke [email protected]

Harvard University• Breivik , Olav Nikolai [email protected]

University of Oslo• Chammartin , Frédérique [email protected]

Swiss TPH• Cseke , Botond [email protected]

University of Edinburgh

• Davíðsson , Ólafur Birgir [email protected]

University of Iceland• Doan , Thinh [email protected]

Trinity College Dublin• Einarsson , Guðmundur [email protected]

University of Iceland• Elvarsson , Bjarki Þór [email protected]

University of Iceland• Fuglstad , Geir-Arne [email protected]

Norwegian University of Science and Technology• Gamerman , Dani [email protected]

UFRJ

• Geirsson , Óli Páll [email protected]


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• Girolami , Mark [email protected]

University College London• Guillot , Gilles [email protected]

Technical University of Denmark• Gunnlaugsson , Thorvaldur [email protected]

Marine Research Institute Iceland• Hlynsson , Hlynur Davíð [email protected]

University of Iceland• Hoveid , Øyvind [email protected]

Norwegian Agricultural Economics Research Institute• Hrafnkelsson , Birgir [email protected]

University of Iceland• Illian , Janine [email protected]

University of St Andrews and University of Trondheim• Illner , Katrin [email protected]

Helmholtz Research Center Munich• Ingebrigtsen , Rikke [email protected]

Norwegian University of Science and Technology• Jacobsen , Robert [email protected]

Aalborg University• Jarosch, Alexander H. [email protected]

University of Iceland• Jónsdóttir , Anna Helga [email protected]

University of Iceland• Jónsson , Hákon [email protected]

University of Copenhagen• Katzfuß , Matthias [email protected]

Texas A&M Unversity• Khan , Emtiyaz [email protected]

École Polytechnique Fédérale de Lausanne• Krivoruchko , Konstantin [email protected]

ESRI• Krainski, Elias T. [email protected]

Norwegian University of Science and Technology• Lenkoski , Alex [email protected]

Norwegian Computing Center• Lindgren , Finn [email protected]

University of Bath

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• Lund , Sigrún Helga [email protected]

University of Iceland• Magnússon , Sigurður Heiðar [email protected]

University of Iceland• Marques , Reinaldo [email protected]

University of Oslo• Martins , Thiago [email protected]

Norwegian University of Science and Technology• Møller , Jesper [email protected]

Aalborg University• Muff , Stefanie [email protected]

University of Zurich• Müller , Peter [email protected]

University of Texas• Myllymäki , Mari [email protected]

Aalto University• Newby , Christopher [email protected]

University of Leicester• Nychka , Douglas [email protected]

National Center for Atmospheric Research• Pétursson , Kjartan Brjánn [email protected]

University of Iceland• Ragnarsson , Birgir Freyr [email protected]

University of Iceland• Riebler , Andrea [email protected]

Norwegian University of Science and Technolog• Roininen , Lassi [email protected]

University of Oulu• Rue , Håvard [email protected]

Norwegian University of Science and Technology• Rúnarsson , Thomas Philip [email protected]


• Rúnarsson , Jón Árni [email protected]

University of Iceland• Särkkä , Simo [email protected]

Aalto University• Sebag , Michele [email protected]

Equipe TAO, CNRS - INRIA - LRI, Université Paris-Sud

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• Shubin , Mikhail [email protected]

University of Helsinki• Sigurðarson , Atli Norðmann [email protected]

University of Iceland• Sigurðarson , Helgi [email protected]

University of Iceland• Simpson , Daniel [email protected]

Norwegian University of Science and Technology• Singh , Warsha [email protected]

University of Iceland• Skaug , Hans J. [email protected]

University of Bergen• Stefánsson , Gunnar [email protected]

University of Iceland• Strathmann , Heiko [email protected]

University College London• Sturludóttir , Erla [email protected]

University of Iceland• Waldmann , Elisabeth [email protected]

Georg-August-Universität Göttingen• Wallin , Jonas [email protected]

Lund University• Wikle , Christopher [email protected]

University of Missouri• Zammit Mangion , Andrew [email protected]

University of Bristol

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Documents

Workshop on Bayesian Inference for Latent Gaussian Models ...gue20/masterfile.pdf · Welcome to the third workshop on Bayesian Inference for Latent Gaussian Models with Applications!