Note on Outbred Studies

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Presentation transcript:

Note on Outbred Studies Interval Mapping Haley, Knott & Elsen (1994) Genetics Thomas & Cortessis (1992) Hum. Hered. Hoeschele & vanRanden (1993ab) Theor. Appl. Genet. (etc.) Guo & Thompson (1994) Biometrics Nuances -- faking it experimental outbred crosses collapse markers from 4 to 2 alleles pedigrees polygenic effects not modeled here related individuals are correlated (via coancestry) June 1999 NCSU QTL Workshop © Brian S. Yandell

NCSU QTL Workshop © Brian S. Yandell What is the Goal Today? show MCMC ideas Gibbs sampler Metropolis-Hastings handle hard problems image analysis genetics large dependent data resampling our data permutation tests MCMC other (bootstrap,…) Bayesian perspective common in animal model use “prior” information previous experiments related genomes inbred lines “easy” can check against *IM ready extension multiple experiments pedigrees non-normal data June 1999 NCSU QTL Workshop © Brian S. Yandell

Basic Idea of Likelihood Use build likelihood in steps build from trait & genotypes at locus likelihood for individual i log likelihood over individuals maximize likelihood (interval mapping) EM method (Lander & Botstein 1989) MCMC method (Guo & Thompson 1994) study whole likelihood as posterior (Bayesian) analytical methods (e.g. Carlin & Louis 1998) MCMC method (Satagopan et al 1996) June 1999 NCSU QTL Workshop © Brian S. Yandell

NCSU QTL Workshop © Brian S. Yandell EM-MCMC duality EM approach can be redone with MCMC EM estimates & maximizes MCMC draws random samples both can address same problem sometimes EM is hard (impossible) to use MCMC is tool of “last resort” use exact methods if you can try other approximate methods be clever! very handy for hard problems in genetics June 1999 NCSU QTL Workshop © Brian S. Yandell

Likelihood & Posterior Example June 1999 NCSU QTL Workshop © Brian S. Yandell

Studying the Likelihood maximize (*IM) find the peak avoid local maxima profile LOD across locus max for effects sample (Bayes) get whole curve summarize later posterior locus & effects together EM method always go up steepest ascent MCMC method jump around go up if you can sometimes go down cool down to find peak simulated annealing simulated tempering June 1999 NCSU QTL Workshop © Brian S. Yandell

NCSU QTL Workshop © Brian S. Yandell Markov chain idea future events given the present state are independent of past events update chain based on current value can make chain arbitrarily complicated chain converges to stable pattern p 1-p 1-q 1 q June 1999 NCSU QTL Workshop © Brian S. Yandell

NCSU QTL Workshop © Brian S. Yandell Markov chain idea p 1-p 1-q 1 q Mitch’s Other June 1999 NCSU QTL Workshop © Brian S. Yandell