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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)

Arguments

Data

list(y, X)

Prior

list(betabar, A, nu, ssq)

Mcmc

list(sigmasq, R, keep, nprint)

Details

Model and Priors

y = Xβ + e with e ~ N(0, σ^2)

β ~ N(betabar, A^{-1})
σ^2 ~ (nu*ssq)/χ^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 σ^2 for first Gibbs sampler draw of β|σ^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)

Value

A list containing:

betadraw

R x k matrix of betadraws

sigmasqdraw

R x 1 vector of sigma-sq draws

Author(s)

Peter Rossi, Anderson School, UCLA, perossichi@gmail.com.

References

For further discussion, see Chapter 3, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.
http://www.perossi.org/home/bsm-1

See Also

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)}

bayesm

Bayesian Inference for Marketing/Micro-Econometrics

v3.1-4
GPL (>= 2)
Authors
Peter Rossi <perossichi@gmail.com>
Initial release
2019-10-14

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