rnmixGibbs {bayesm} | R Documentation |
rnmixGibbs
implements a Gibbs Sampler for normal mixtures.
rnmixGibbs(Data, Prior, Mcmc)
Data |
list(y) |
Prior |
list(Mubar,A,nu,V,a,ncomp) (only ncomp required) |
Mcmc |
list(R,keep) (R required) |
Model:
y_i ~ N(mu_{ind_i},Sigma_{ind_i}).
ind ~ iid multinomial(p). p is a ncomp x 1 vector of probs.
Priors:
mu_j ~ N(mubar,Sigma_j (x) A^{-1}). mubar=vec(Mubar).
Sigma_j ~ IW(nu,V).
note: this is the natural conjugate prior – a special case of multivariate
regression.
p ~ Dirchlet(a).
Output of the components is in the form of a list of lists.
compsdraw[[i]] is ith draw – list of ncomp lists.
compsdraw[[i]][[j]] is list of parms for jth normal component.
jcomp=compsdraw[[i]][j]]. Then jth comp ~ N(jcomp[[1]],Sigma),
Sigma = t(R)%*%R, R^{-1} = jcomp[[2]].
List arguments contain:
nmix |
{a list containing: probdraw,zdraw,compdraw}
more details on contents of nmix:
In this model, the component normal parameters are not-identified due to label-switching.
However, the fitted mixture of normals density is identified as it is invariant to label-switching.
See Allenby et al, chapter 5 for details. Use eMixMargDen
or momMix
to compute
posterior expectation or distribution of various identified parameters.
Peter Rossi, Graduate School of Business, University of Chicago, Peter.Rossi@ChicagoGsb.edu.
For further discussion, see Bayesian Statistics and Marketing
by Rossi, Allenby and McCulloch, Chapter 3.
http://faculty.chicagogsb.edu/peter.rossi/research/bsm.html
rmixture
, rmixGibbs
,eMixMargDen
, momMix
,
mixDen
, mixDenBi
## if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10} set.seed(66) dim=5; k=3 # dimension of simulated data and number of "true" components sigma = matrix(rep(0.5,dim^2),nrow=dim);diag(sigma)=1 sigfac = c(1,1,1);mufac=c(1,2,3); compsmv=list() for(i in 1:k) compsmv[[i]] = list(mu=mufac[i]*1:dim,sigma=sigfac[i]*sigma) comps = list() # change to "rooti" scale for(i in 1:k) comps[[i]] = list(mu=compsmv[[i]][[1]],rooti=solve(chol(compsmv[[i]][[2]]))) pvec=(1:k)/sum(1:k) nobs=500 dm = rmixture(nobs,pvec,comps) Data1=list(y=dm$x) ncomp=9 Prior1=list(ncomp=ncomp) Mcmc1=list(R=R,keep=1) out=rnmixGibbs(Data=Data1,Prior=Prior1,Mcmc=Mcmc1) cat("Summary of Normal Mixture Distribution",fill=TRUE) summary(out) tmom=momMix(matrix(pvec,nrow=1),list(comps)) mat=rbind(tmom$mu,tmom$sd) cat(" True Mean/Std Dev",fill=TRUE) print(mat) if(0){ ## ## plotting examples ## plot(out) }