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Applications and Summary

Applications and Summary. Presented By Dan Geiger Journal Club of the Pharmacogenetics Group Meeting Technion. Rare Recessive Diseases. Pedigree 1C. A.

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Applications and Summary

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  1. Applications and Summary .

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

  3. Rare Recessive Diseases Pedigree 1C 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)? .

  4. Modeling The IBD Process L X1 X2 XL-1 XL Xi 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. .

  5. Adding genomic data X1 X2 XL-1 XL Xk Y1 Y2 YL-1 YL Yk .

  6. X1 X2 XL-1 XL Xi Y1 Y2 YL-1 YL Yi Computing IBD from genomic data P(y1,…,yL, x1,…,xL) 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) = xiP(y1,…,yL,xi). Posterior IBD Probabilities: P(xi | y1,…,yL) = P(y1,…,yL,xi)/ xiP(y1,…,yL,xi).

  7. Simulation Results For First Degree Cousins (1C) .

  8. Gene mapping: The FLOD score P(Homozigosity for allele of frequency q at location Xi) = q P(Xk=1 | Y) + q2P(Xk = 0 | Y) P(Homozigosity for allele of frequency q by random) = qf + q2(1-f) Total FLOD score is the sum of the FLOD for all individuals. .

  9. The Taybi-Linder Syndrome .

  10. Data and Inbreeding Coeffcients .

  11. LOD and FLOD results genomewise .

  12. LOD and FLOD results for Chromosome 2 FLOD FLODe4 LOD .

  13. LOD and FLOD results for Chromosome 7 FLODe4 LOD FLOD .

  14. 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

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