Posterior sampling for regression parameters
Gibbs sampler for linear, generalized linear and survival models under product non-local priors, Zellner's prior and a Normal approximation to the posterior. Both sampling conditional on a model and Bayesian model averaging are implemented (see Details).
If x and y not specified samples from non-local priors/posteriors with density proportional to d(theta) N(theta; m, V) are produced, where d(theta) is the non-local penalty term.
rnlp(y, x, m, V, msfit, outcometype, family, priorCoef, priorGroup, priorVar, isgroup, niter=10^3, burnin=round(niter/10), thinning=1, pp='norm')
y: Vector with observed responses. When class(y)=='Surv'
sampling is based on the Cox partial likelihood, else a linear model is assumed.
x: Design matrix with all potential predictors
m: Mean for the Normal kernel
V: Covariance for the Normal kernel
msfit: Object of class msfit returned by modelSelection. If specified Bayesian model averaging posterior samples are returned, according to posterior model probabilities in msfit, and then arguments y, x, m, V etc. If msfit is missing then posterior samples under the full model y ~ x are returned
outcometype: Type of outcome. Possible values are "Continuous", "glm" or "Survival"
family: Assumed family for the family. Some possible values are "normal", "binomial logit" and "Cox"
priorCoef: Prior distribution for the coefficients. Ignored if msfit is supplied. Must be object of class msPriorSpec, e.g. created by momprior, emomprior, imomprior, zellnerprior
priorGroup: Prior on grouped coefficients (e.g. categorical predictors with >2 categories, splines), as passed to modelSelection
priorVar: Prior on residual variance. Ignored if msfit
supplied. Must be object of class msPriorSpec, e.g. created with igprior
isgroup: Logical vector where TRUE indicates that the variable is part of a group, e.g. one of several dummy indicators for a discrete covariate
niter: Number of MCMC iterations
burnin: Number of burn-in MCMC iterations. Defaults to .1*niter. Set to 0 for no burn-in
thinning: MCMC thinning factor, i.e. only one out of each thinning iterations are reported. Defaults to no thinning
pp: When msfit is provided this is the method to compute posterior model probabilities, which determine the sampled models. Can be 'norm' or 'exact', see postProb for details.
The algorithm is implemented for product MOM (pMOM), product iMOM (piMOM) and product eMOM (peMOM) priors. The algorithm combines an orthogonalization that provides low serial correlation with a latent truncation representation that allows fast sampling.
When y and x are specified sampling is for the linear regression posterior. When argument msfit is left missing, posterior sampling is for the full model regressing y on all covariates in x. When msfit is specified each model is drawn with probability given by postProb(msfit). In this case, a Bayesian Model Averaging estimate of the regression coefficients can be obtained by applying colMeans to the rnlp ouput matrix.
When y and x are left missing, sampling is from a density proportional to d(theta) N(theta; m,V), where d(theta) is the non-local penalty (e.g. d(theta)=prod(theta^(2r)) for the pMOM prior).
Matrix with posterior samples
D. Rossell and D. Telesca. Non-local priors for high-dimensional estimation, 2014. http://arxiv.org/pdf/1402.5107v2.pdf
David Rossell
modelSelection to perform model selection and compute posterior model probabilities. For more details on prior specification see msPriorSpec-class.
#Simulate data x <- matrix(rnorm(100*3),nrow=100,ncol=3) theta <- matrix(c(1,1,0),ncol=1) y <- x %*% theta + rnorm(100) fit1 <- modelSelection(y=y, x=x, center=FALSE, scale=FALSE) th <- rnlp(msfit=fit1, niter=100) colMeans(th)