bayesm (version 3.1-6)

runiregGibbs: Gibbs Sampler for Univariate Regression

Description

runiregGibbs implements a Gibbs Sampler to draw from posterior of a univariate regression with a conditionally conjugate prior.

Usage

runiregGibbs(Data, Prior, Mcmc)

Value

A list containing:

betadraw

\(R x k\) matrix of betadraws

sigmasqdraw

\(R x 1\) vector of sigma-sq draws

Arguments

Data

list(y, X)

Prior

list(betabar, A, nu, ssq)

Mcmc

list(sigmasq, R, keep, nprint)

Author

Peter Rossi, Anderson School, UCLA, .

Details

Model and Priors

\(y = X\beta + e\) with \(e\) \(\sim\) \(N(0, \sigma^2)\)

\(\beta\) \(\sim\) \(N(betabar, A^{-1})\)
\(\sigma^2\) \(\sim\) \((nu*ssq)/\chi^2_{nu}\)

Argument Details

Data = list(y, X)

y:	\(n x 1\) vector of observations
X:	\(n x k\) design matrix

Prior = list(betabar, A, nu, ssq) [optional]

betabar:	\(k x 1\) prior mean (def: 0)
A:	\(k x k\) prior precision matrix (def: 0.01*I)
nu:	d.f. parameter for Inverted Chi-square prior (def: 3)
ssq:	scale parameter for Inverted Chi-square prior (def: var(y))

Mcmc = list(sigmasq, R, keep, nprint) [only R required]

sigmasq:	value for \(\sigma^2\) for first Gibbs sampler draw of \(\beta\)|\(\sigma^2\)
R:	number of MCMC draws
keep:	MCMC thinning parameter -- keep every keepth draw (def: 1)
nprint:	print the estimated time remaining for every nprint'th draw (def: 100, set to 0 for no print)

References

For further discussion, see Chapter 3, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.

See Also

runireg

Examples

if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=1000} else {R=10}
set.seed(66)

n = 200
X = cbind(rep(1,n), runif(n))
beta = c(1,2)
sigsq = 0.25
y = X%*%beta + rnorm(n,sd=sqrt(sigsq))

out = runiregGibbs(Data=list(y=y, X=X), Mcmc=list(R=R))

cat("Summary of beta and Sigmasq draws", fill=TRUE)
summary(out$betadraw, tvalues=beta)
summary(out$sigmasqdraw, tvalues=sigsq)

## plotting examples
if(0){plot(out$betadraw)}