Bayesian Statistics

Julyan Arbeljulyan.arbel@carloalberto.org

Collegio Carlo Alberto, Moncalieri, Italy

March 17, 2015

Students are to choose one paper in the following list, or possibly outsideof the list upon my agreement. The papers are available online. Most of themare collected in this zip file. The presentation can focus on a particular section/ result / example of the paper. Evaluation of the students is based on theunderstanding and presentation of the chosen paper.

Remark: The Annals of Statistics and The Annals of Probability are theoret-ical journals, while The American Statistician, American Scientist and Statisti-cal Science are rather general audience journals. You can find a brief descriptionof the journals by following the links below:

The Annals of Probability, The Annals of Statistics, Bayesian Analysis,Biometrika, Journal of the American Statistical Association, Journal of theRoyal Statistical Society Series B (Statistical Methodology), The AmericanStatistician, American Scientist, Statistical Science.

References

[1] T. Bayes. An essay towards solving a problem in the doctrine of chances.Philosophical Transactions (1683-1775), pages 370–418, 1763.

[2] W Keith Hastings. Monte Carlo sampling methods using Markov chainsand their applications. Biometrika, 57(1):97–109, 1970.

[3] Dennis V Lindley and Adrian FM Smith. Bayes estimates for the lin-ear model. Journal of the Royal Statistical Society: Series B (StatisticalMethodology), pages 1–41, 1972.

[4] Thomas S Ferguson. A Bayesian analysis of some nonparametric problems.The Annals of Statistics, pages 209–230, 1973.

[5] Jose M Bernardo. Reference posterior distributions for Bayesian inference.Journal of the Royal Statistical Society: Series B (Statistical Methodology),pages 113–147, 1979.

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[6] Persi Diaconis and Donald Ylvisaker. Conjugate priors for exponentialfamilies. The Annals of Statistics, 7(2):269–281, 1979.

[7] Irving J Good. AM Turing’s statistical work in World War II. Biometrika,pages 393–396, 1979.

[8] Persi Diaconis and David Freedman. Finite exchangeable sequences. TheAnnals of Probability, pages 745–764, 1980.

[9] Charles M Stein. Estimation of the mean of a multivariate normal distri-bution. The Annals of Statistics, pages 1135–1151, 1981.

[10] Donald B Rubin. Bayesianly justifiable and relevant frequency calculationsfor the applies statistician. The Annals of Statistics, 12(4):1151–1172, 1984.

[11] Persi Diaconis and Donald Ylvisaker. Quantifying prior opinion. BayesianStatistics, 2:133–156, 1985.

[12] Persi Diaconis and David Freedman. On the consistency of Bayes estimates.The Annals of Statistics, pages 1–26, 1986.

[13] Persi Diaconis. Recent progress on de Finetti’s notions of exchangeability.Bayesian statistics, 3:111–125, 1988.

[14] Robert Tibshirani. Noninformative priors for one parameter of many.Biometrika, 76(3):604–608, 1989.

[15] Sandy Zabell. RA Fisher on the history of inverse probability. StatisticalScience, pages 247–256, 1989.

[16] Alan E Gelfand and Adrian FM Smith. Sampling-based approaches to cal-culating marginal densities. Journal of the American statistical Association,85(410):398–409, 1990.

[17] Eric L Lehmann. Model specification: the views of Fisher and Neyman,and later developments. Statistical Science, 5(2):160–168, 1990.

[18] Dennis V Lindley. The present position in Bayesian statistics. StatisticalScience, pages 44–65, 1990.

[19] CJ Geyer. Practical Monte Carlo Markov chain (with discussion). Statis-tical Science, 7(1):473–511, 1992.

[20] William H Jefferys and James O Berger. Ockham’s razor and Bayesiananalysis. American Scientist, pages 64–72, 1992.

[21] Eugene Seneta. Lewis Carroll’s “pillow problems”: on the 1993 centenary.Statistical science, pages 180–186, 1993.

[22] David Madigan, Jeremy York, and Denis Allard. Bayesian graphical modelsfor discrete data. International Statistical Review/Revue Internationale deStatistique, pages 215–232, 1995.

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[23] Robert E Kass and Larry Wasserman. The selection of prior distribu-tions by formal rules. Journal of the American Statistical Association,91(435):1343–1370, 1996.

[24] Felix Abramovich, Theofanis Sapatinas, and Bernard W Silverman.Wavelet thresholding via a Bayesian approach. Journal of the Royal Sta-tistical Society: Series B (Statistical Methodology), 60(4):725–749, 1998.

[25] James O Berger. Bayesian analysis: A look at today and thoughts oftomorrow. Journal of the American Statistical Association, 95(452):1269–1276, 2000.

[26] L Zhao. Bayesian aspects of some nonparametric problems. The Annals ofStatistics, 28(2):532–552, Jan 2000.

[27] Stephen G Walker and Nils Lid Hjort. On Bayesian consistency. Journal ofthe Royal Statistical Society: Series B (Statistical Methodology), 63(4):811–821, 2001.

[28] Bradley Efron. Bayesians, frequentists, and scientists. Journal of the Amer-ican Statistical Association, 100(469):1–5, 2005.

[29] Roderick J Little. Calibrated Bayes: a Bayes/frequentist roadmap. TheAmerican Statistician, 60(3):213–223, 2006.

[30] Gerard Letac and Helene Massam. Wishart distributions for decomposablegraphs. The Annals of Statistics, 35(3):1278–1323, 2007.

[31] Stephen G Walker, Antonio Lijoi, and Igor Prunster. On rates of conver-gence for posterior distributions in infinite-dimensional models. The Annalsof Statistics, 35(2):738–746, 2007.

[32] Christian Robert and George Casella. A short history of Markov ChainMonte Carlo: subjective recollections from incomplete data. StatisticalScience, 26(1):102–115, 2011.

[33] Peter Muller and Riten Mitra. Bayesian nonparametric inference–why andhow. Bayesian Analysis, 8(2), 2013.

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