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\name{rbiNormGibbs}
\alias{rbiNormGibbs}
\concept{bayes}
\concept{Gibbs Sampling}
\concept{MCMC}
\concept{normal distribution}
\title{Illustrate Bivariate Normal Gibbs Sampler}
\description{
\code{rbiNormGibbs} implements a Gibbs Sampler for the bivariate normal distribution. Intermediate moves are plotted and the output is contrasted with the iid sampler. This function is designed for illustrative/teaching purposes.}
\usage{rbiNormGibbs(initx=2, inity=-2, rho, burnin=100, R=500)}
\arguments{
\item{initx }{ initial value of parameter on x axis (def: 2)}
\item{inity }{ initial value of parameter on y axis (def: -2)}
\item{rho }{ correlation for bivariate normals}
\item{burnin }{ burn-in number of draws (def: 100)}
\item{R }{ number of MCMC draws (def: 500)}
}
\details{
\eqn{(\theta_1, \theta_2) ~ N( (0,0), \Sigma}) with \eqn{\Sigma} = \code{matrix(c(1,rho,rho,1),ncol=2)}
}
\value{
\eqn{R x 2} matrix of draws
}
\author{Peter Rossi, Anderson School, UCLA, \email{perossichi@gmail.com}.}
\references{For further discussion, see Chapters 2 and 3, \emph{Bayesian Statistics and Marketing} by Rossi, Allenby, and McCulloch.}
\examples{
\dontrun{out=rbiNormGibbs(rho=0.95)}
}
\keyword{distribution}
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