. Applications and Summary

. Presented By Dan Geiger Journal Club of the Pharmacogenetics Group Meeting Technion

. Rare Recessive Diseases A 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

. X1X1 X2X2 X L-1 XLXL XiXi L Assumptions: No interferance, No errors in genetic maps.  ={ a, f } are parameters that can be estimated (e.g. by ML), if IBD data is available. No change of coancestry Modeling The IBD Process

. X1X1 X2X2 X L-1 XLXL Y1Y1 Y2Y2 Y L-1 YLYL XkXk YkYk Adding genomic data

6 Computing IBD from genomic data X1X1 X2X2 X L-1 XLXL Y1Y1 Y2Y2 Y L-1 YLYL XiXi YiYi Forward-Backward formula: P  (y 1,…,y L,x i ) = P  (y 1,…,y i,x i ) P  (y i+1,…,y L | x i )  f(x i ) b(x i ) Likelihood of Evidence: P  (y 1,…,y L ) =  xi P  (y 1,…,y L,x i ). Posterior IBD Probabilities: P  (x i | y 1,…,y L ) = P  (y 1,…,y L,x i )/  xi P  (y 1,…,y L,x i ). P  (y 1,…,y L, x 1,…,x L )

. Simulation Results For First Degree Cousins (1C)

. P(Homozigosity for allele of frequency q by random) = qf + q 2 (1-f) P(Homozigosity for allele of frequency q at location X i ) = q P(X k =1 | Y) + q 2 P(X k = 0 | Y) Gene mapping: The FLOD score Total FLOD score is the sum of the FLOD for all individuals.

. The Taybi-Linder Syndrome

. Data and Inbreeding Coeffcients

. LOD and FLOD results genomewise

. LOD and FLOD results for Chromosome 2 FLOD FLODe4 LOD

. LOD and FLOD results for Chromosome 7 FLOD LOD FLODe4

. Haplotype Analysis

15 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

16 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