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Applications and Summary

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Presented By Dan GeigerJournal Club of the Pharmacogenetics Group Meeting

Technion

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Rare Recessive Diseases

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Given such pedigree our program Superlink produces a LOD score determining if this is a coincidence or suggestive of disease gene location. How probable is it to be IBD (denoted f) ?

Pedigree 1C

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X1 X2 XL-1 XLXi

L

Assumptions: No interferance, No errors in genetic maps.={ a , f } are parameters that can be estimated (e.g. by ML), ifIBD data is available.

No change of coancestry

Modeling The IBD Process

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X1 X2 XL-1 XL

Y1 Y2 YL-1 YL

Xk

Yk

Adding genomic data

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Computing IBD from genomic data

X1 X2 XL-1 XL

Y1 Y2 YL-1 YL

Xi

Yi

Forward-Backward formula:P(y1,…,yL,xi) = P(y1,…,yi,xi) P(yi+1,…,yL | xi) f(xi) b(xi)

Likelihood of Evidence:

P(y1,…,yL) = xi P(y1,…,yL,xi).

Posterior IBD Probabilities:

P(xi | y1,…,yL) = P(y1,…,yL,xi)/ xi P(y1,…,yL,xi).

P(y1,…,yL, x1,…,xL)

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Simulation Results For First Degree Cousins (1C)

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P(Homozigosity for allele of frequency q by random) = qf + q2(1-f)

P(Homozigosity for allele of frequency q at location Xi) = q P(Xk=1 | Y) + q2P(Xk = 0 | Y)

Gene mapping: The FLOD score

Total FLOD score is the sum of the FLOD for all individuals.

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The Taybi-Linder Syndrome

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Data and Inbreeding Coeffcients

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LOD and FLOD results genomewise

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LOD and FLOD results for Chromosome 2

FLOD

FLODe4LOD

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LOD and FLOD results for Chromosome 7

FLOD

LOD

FLODe4

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Haplotype Analysis

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Road Map For Graphical Models•Foundations

• Probability theory –subjective versus objective• Other formalisms for uncertainty (Fuzzy, Possibilistic, belief functions)•Type of graphical models: Directed, Undirected, Chain Graphs, Dynamic networks, factored HMM, etc• Discrete versus continuous distributions• Causality versus correlation

•Inference•Exact Inference

• Variable elimination, clique trees, message passing• Using internal structure like determinism or zeroes• Queries: MLE, MAP, Belief update, sensitivityApproximate Inference•Sampling methods•Loopy propagation (minimizing some energy function)• Variational method

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Road Map For Graphical Models

•Learning•Complete data versus incomplete data•Observed variables versus hidden variables•Learning parameters versus learning structure•Scoring methods versus conditional independence tests methods•Exact scores versus asymptotic scores•Search strategies vs. Optimal learning of trees/polytrees/TANs

•Applications• Diagnostic tools: printer problems to airplanes failures• Medical diagnostic • Error correcting codes: Turbo codes• Image processing• Applications in Bioinformatics: gene mapping, regulatory, metabolic, and other network learning