Applications and Summary .
Presented By Dan Geiger Journal Club of the Pharmacogenetics Group Meeting Technion.
Rare Recessive Diseases Pedigree 1 C 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) ?
Modeling The IBD Process X 1 X 2 Xi XL-1 XL L No change of coancestry . 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.
Adding genomic data X 1 Xk XL-1 XL Y 1 . X 2 Yk YL-1 YL
Computing IBD from genomic data P (y 1, …, y. L, x 1, …, x. L) X 1 X 2 Xi XL-1 XL Y 1 Y 2 Yi YL-1 YL Forward-Backward formula: P (y 1, …, y. L, xi) = P (y 1, …, yi, xi) P (yi+1, …, y. L | xi) f(xi) b(xi) Likelihood of Evidence: P (y 1, …, y. L) = xi P (y 1, …, y. L, xi). Posterior IBD Probabilities: P (xi | y 1, …, y. L) = P (y 1, …, y. L, xi)/ xi P (y 1, …, y. L, xi). 6
Simulation Results For First Degree Cousins (1 C) .
Gene mapping: The FLOD score P(Homozigosity for allele of frequency q at location Xi) = q P(Xk=1 | Y) + q 2 P(Xk = 0 | Y) P(Homozigosity for allele of frequency q by random) = qf + q 2(1 -f) 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 FLODe 4 LOD .
LOD and FLOD results for Chromosome 7 FLODe 4 LOD FLOD .
Haplotype Analysis .
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, sensitivity. Approximate Inference • Sampling methods • Loopy propagation (minimizing some energy function) • Variational method 15
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 16
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