plotSampRep-method: Plot the sampling representation of component parameters

In simonsays1980/finmix: An R package for Bayesian estimation of finite mixture distributions

Description

Calling plotSampRep() on an object of class mcmcoutput or mcmcoutputperm plots the sampling representation of the sampled component parameters from MCMC sampling, either the original parameters or the relabeled ones (mcmcoutputperm).

Arguments

x	An mcmcoutput or mcmcoutputperm object containing all sampled values.
dev	A logical indicating, if the plots should be shown by a graphical device. If plots should be stored to a file set dev to FALSE.
...	Further arguments to be passed to the plotting function.

Details

To visualize the posterior density of the component parameters the MCMC draws are used as a sampling representation. Each combination of component parameters is plotted in a scatter to visualize the contours of the posterior density. For bivariate component parameters this could also be done by estimating and plotting the density directly, but for higher-dimensional parameter vectors this is not anymore possible and so sampling representations define a proper solution for visualization and allow us to study how a specific dimension of the parameter vector differs among the various components of the mixture distribution. If this element is significantly different among components we will observe K(K-1) modes in the sampling representation. On the other side, if this element is mainly the same among the components of the mixture, we will rather observe a single cluster.

As Frühwirth-Schnatter (2006) writes, "One informal method for diagnosing mixtures is mode hunting in the mixture posterior density (Frühwirth-Schnatter, 2001b). It is based on the observation that with an increasing number of observations, the mixture likelihood function has K! dominant modes if the data actually arise from a finite mixture distribution with K components, and that less than K! dominant modes are present if the finite mixture model is overfitting the number of components." The sampling representation helps to perform this mode hunting in practice.

Note that this method for mcmcoutputperm objects is only implemented for mixtures of Poisson and Binomial distributions.

Value

The sampling representation of the MCMC samples.

References

• Frühwirth-Schnatter (2006), "Finite Mixture and Markov Switching Models"

• Frühwirth-Schnatter, S. (2001b), "Markov chain Monte Carlo estimation of classical and dynamic switching and mixture models." Journal of the American Statistical Association 96, 194–209.

See Also

• mixturemcmc() for performing MCMC sampling

• mcmcpermute() for permuting MCMC samples

• plotTraces() for plotting the traces of sampled values

• plotHist() for plotting histograms of sampled values

• plotDens() for plotting densities of sampled values

• plotPointProc() for plotting the point process of sampled values

• plotPostDens() for plotting posterior densities for sampled values

Examples

# Define a Poisson mixture model with two components.
f_model <- model("poisson", par = list(lambda = c(0.3, 1.2)), K = 2)
# Simulate data from the mixture model.
f_data <- simulate(f_model)
# Define the hyper-parameters for MCMC sampling.
f_mcmc <- mcmc()
# Define the prior distribution by relying on the data.
f_prior <- priordefine(f_data, f_model)
# Start MCMC sampling.
f_output <- mixturemcmc(f_data, f_model, f_prior, f_mcmc)
plotSampRep(f_output)

simonsays1980/finmix documentation built on Dec. 23, 2021, 2:25 a.m.