SM.MixPois: summary of the output produced by K.MixPois

In Ultimixt: Bayesian Analysis of Location-Scale Mixture Models using a Weakly Informative Prior

Description

This generic function summarizes the MCMC samples produced by K.MixPois when several estimation methods have been invoked depending on the unimodality or multimodality of the argument.

Usage

SM.MixPois(estimate, xobs)

Arguments

estimate	output of K.MixPois
xobs	vector of observations

Details

The output of this function contains posterior point estimates for all parameters of the reparameterized Poisson mixture model. It summarizes unimodal MCMC samples by computing measures of centrality, including mean and median, while multimodal outputs require a preprocessing, due to the label switching phenomenon (Jasra et al., 2005). The summary measures are then computed after performing a multi-dimensional k-means clustering (Hartigan and Wong, 1979) following the suggestion of Fruhwirth-Schnatter (2006).

Value

lambda	vector of mean and median of simulated draws from the conditional posterior of the mixture model mean
gamma.i	vector of mean and median of simulated draws from the conditional posterior of the component mean hyperparameters; i=1, …, k
weight.i	vector of mean and median of simulated draws from the conditional posterior of the component weights of the mixture distribution; i=1, …, k
lambda.i	vector of mean and median of simulated draws from the conditional posterior of the component means of the mixture distribution; i=1, …, k
Acc rat	vector of final acceptance rate of the proposal distributions of the algorithm with no calibration stage for the proposal scales
Opt scale	vector of optimal proposal scales obtained the by calibration stage

Note

For multimodal outputs such as the mixture model weights, component means, and component mean hyperparameters, for each MCMC draw, first the labels of the weights p_i, i=1, …, k and corresponding component means are permuted in such a way that p_1≤ … ≤ p_k. Then the posterior component means are partitioned into k clusters by applying a standard k-means algorithm with k clusters, following Fruhwirth-Schnatter (2006) method. The obtained classification sequence was then used to reorder and identify the other component-specific parameters, namely component mean hyperparameters and weights. For each group, cluster centers are considered as parameter estimates.

Author(s)

Kaniav Kamary

References

Jasra, A., Holmes, C. and Stephens, D. (2005). Markov Chain Monte Carlo methods and the label switching problem in Bayesian mixture modeling. Statistical Science, 20, 50–67.

Hartigan, J. A. and Wong, M. A. (1979). A K-means clustering algorithm. Applied Statistics 28, 100–108.

Fruhwirth-Schnatter, S. (2006). Finite mixture and Markov switching models. Springer-Verlag.

See Also

K.MixPois

Examples

N=500
U =runif(N)                                            
xobs = rep(NA,N)
for(i in 1:N){
    if(U[i]<.6){
        xobs[i] = rpois(1,lambda=1)
    }else{
        xobs[i] = rpois(1,lambda=5)
    }
}
#estimate=K.MixPois(xobs, k=2, alpha0=.5, alpha=.5, Nsim=10000)
#SM.MixPois(estimate, xobs)
#plot(estimate[[8]][,1],estimate[[2]][,1],pch=19,col="skyblue",cex=0.5,xlab="lambda",ylab="p")
#points(estimate[[8]][,2], estimate[[2]][,2], pch=19, col="gold", cex=0.5)
#points(c(1,5), c(0.6,0.4), pch=19, cex=1)

Example output

Loading required package: coda
Loading required package: gtools

Ultimixt documentation built on May 1, 2019, 10:56 p.m.