swapbc1: Sample BC1 or Recombinant Inbred loci via approximate posterior.

Description

An MCMC sampler for loci using precomputed dispersion matrices, various priors, and a pre-selected set of variables. For use with BC1 (backcross) designs and recombinant inbred lines.

Usage

swapbc1(varcov, invars, rparm, nreps, ana.obj, locs=seq(ncol(var.x)),
locs.prior=rep(1, ncol(var.x)),tol=1e-10 )

Arguments

varcov

The result of make.varcov

rparm

Scalar or vector with nrow(varcov$var.x) elements; the 'ridge' parameters for the independent variables - larger values imply more shrinkage or a more concentrated prior for the regresion coefficients.

nreps

How many cycles of MCMC to perform

ana.obj

A object produced by make.analysis.obj

invars

Which variables to start in the model. The first of these is immediately removed, so it is merely a placeholder. The number of genes in the model is therefore k <- length(invars)

locs

The columns of varcov$var.x to use. The default uses all of them.

locs.prior

The prior mass to associate with each variable. Typically, these sum to one, but sometimes they might each be set to one (as in computing lod scores).

tol

Used in forming QR decomposition. Let it be.

Value

A list with components:
configA k by k by nreps array of the locations sampled in each iteration.
posteriorsA vector of length k*nreps with the posteriors of the models.
coefsA k by k matrix of the regression coefficients.
callThe call to swapbc1
condThe k*nreps posterior probabilities of the k-1 gene models.
margThe k*nreps marginal posteriors for all k gene models that could be formed using the current k-1 gene model
alt.marginalA vector with length(locs) elements. At each step, the posterior associated with each candidate locus is added to an element of this vector. After all steps are finished, the result is normalized to sum to one. This turns out to be an exceedingly stable estimate of the marginal posterior.
alt.coefA vector with length(locs) elements. At each step, the product of each posterior times the coefficient associated with a candidate locus is added to an element of this vector. After all steps are finished, the result is normalized by the total marginal posterior. This turns out to be an exceedingly stable estimate of the marginal (over all models) posterior mean of the regression coefficients.

keywords

utilities

Details

An MCMC sampler for loci using the object of make.varcov is executed. This sampler uses the exact posterior probability under the assumed correctness of the regression model using expected genotypes given marker values. This amounts to linearizing the likelihood with respect to the (possibly unknown) locus states. For models where the loci are fully informative markers this is the true posterior.

The chain is implemented as follows: given a set of regressor variables to start, one variable is removed, all regressor variables not in the model are examined to determine the effect of each on the posterior. One variable is sampled. The process is repeated until each variable has been removed and a new one sampled in its place (possibly the same variable that was removed is sampled). And this whole cycle is repeated nreps times.

References

Berry C.C. (1998) Computationally Efficient Bayesian QTL Mapping in Experimental Crosses. ASA Proceedings of the Biometrics Section, 164-169.