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Applications and Summary
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Presented By Dan Geiger
Journal Club of the Pharmacogenetics Group Meeting
Technion
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Rare Recessive Diseases
Pedigree 1C
A
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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) ?
Modeling The IBD Process
X1
X2
Xi
XL-1
XL
L
No change of coancestry
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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
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X1
X2
Xk
XL-1
XL
Y1
Y2
Yk
YL-1
YL
Computing IBD from genomic data
P(y1,…,yL, x1,…,xL)
X1
X2
Xi
XL-1
XL
Y1
Y2
Yi
YL-1
YL
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).
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Simulation Results For First
Degree Cousins (1C)
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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.
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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
FLODe4
LOD
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LOD and FLOD results for
Chromosome 7
FLODe4
LOD
FLOD
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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
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