rnlp: Posterior sampling for regression parameters
In mombf: Bayesian Model Selection and Averaging for Non-Local and Local Priors

Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1 2	rnlp(y, x, m, V, msfit, outcometype, family, priorCoef, priorGroup, priorVar, 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`
`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

David Rossell

D. Rossell and D. Telesca. Non-local priors for high-dimensional estimation, 2014. http://arxiv.org/pdf/1402.5107v2.pdf

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)