drawPosteriorParallel: Draw from Posterior Parallel Distribution

In scalablebayesm: Distributed Markov Chain Monte Carlo for Bayesian Inference in Marketing

Draw from Posterior Parallel Distribution

Description

drawPosteriorParallel draws from a posterior predictive distribution.

Usage

drawPosteriorParallel(draws, Z, Prior, Mcmc)

Arguments

draws	(list) - a list of length s where each sublist contains compdraw,
Z	(matrix) - (optional) an nreg/s \times nz matrix of unit characteristics
Prior	(list) - (optional) a list of optional parameters 'v' and 'nu'
Mcmc	(list) - a list containing 'R' and optionally 'keep'

Value

A list containing:

• betadraw: A matrix of size R \times nvar containing the drawn beta values from the Gibbs sampling procedure.

Author(s)

Federico Bumbaca, Leeds School of Business, University of Colorado Boulder, [e-mail]

Federico Bumbaca, [e-mail]

References

Bumbaca, F. (Rico), Misra, S., & Rossi, P. E. (2020). Scalable Target Marketing: Distributed Markov Chain Monte Carlo for Bayesian Hierarchical Models. Journal of Marketing Research, 57(6), 999-1018.

Examples

s=1
R=2000
nreg = 2000
nobs=5 #number of observations
nvar=3 #columns
nz=2

Z=NULL
Delta=matrix(c(1,0,1,0,1,2),ncol=nz) 
tau0=1
iota=c(rep(1,nobs)) 

## create arguments for rmixture

#Default
tcomps=NULL
a = diag(1, nrow=3)
tcomps[[1]] = list(mu=c(0,-1,-2),rooti=a) 
tpvec = 1                             
ncomp=length(tcomps)

regdata=NULL
betas=matrix(double(nreg*nvar),ncol=nvar) 
tind=double(nreg) 

for (reg in 1:nreg) { 
 tempout=bayesm::rmixture(1,tpvec,tcomps)
 if (is.null(Z)){
   betas[reg,]= as.vector(tempout$x)  
 }else{
   betas[reg,]=Delta%*%Z[reg,]+as.vector(tempout$x)} 
 tind[reg]=tempout$z
 X=cbind(iota,matrix(runif(nobs*(nvar-1)),ncol=(nvar-1))) 
 tau=tau0*runif(1,min=0.5,max=1) 
 y=X%*%betas[reg,]+sqrt(tau)*rnorm(nobs)
 regdata[[reg]]=list(y=y,X=X,beta=betas[reg,],tau=tau) 
}

Prior1=list(ncomp=ncomp) 
keep=1
Mcmc1=list(R=R,keep=keep)
Data1=list(list(regdata=regdata,Z=Z))


Data2 = partition_data(Data1, s)

draws = parallel::mclapply(Data2, FUN = rhierLinearMixtureParallel, Prior = Prior1, Mcmc = Mcmc1, 
mc.cores = s, mc.set.seed = TRUE)

out = parallel::mclapply(draws,FUN=drawPosteriorParallel,
Z=Z, Prior = Prior1, Mcmc = Mcmc1, mc.cores=s,
mc.set.seed = TRUE)

scalablebayesm documentation built on April 3, 2025, 7:55 p.m.