Bayesian estimation of a very general model class, where the distribution of the observations depends on a latent process taking values in a discrete state space, is discussed in this article. This model class covers finite mixture modeling, Markov switching autoregressive modeling, and dynamic linear models with switching. The consequences the unidentifiability of this type of model has on Markov chain Monte Carlo (MCMC) estimation are explicitly dealt with. Joint Bayesian estimation of all latent variables, model parameters, and parameters that determine the probability law of the latent process is carried out by a new MCMC method called permutation sampling. The permutation sampler first samples from the unconstrained posterior–which often can be done in a convenient multimove manner–and then applies a permutation of the current labeling of the states of the latent process. In a first run, the random permutation sampler used selected the permutation randomly. The MCMC output of the random permutation s...

Skew-normal and skew-t distributions have proved to be useful for capturing skewness and kurtosis in data directly without transformation. Recently, finite mixtures of such distributions have been considered as a more general tool for handling heterogeneous data involving asymmetric behaviors across subpopulations. We consider such mixture models for both univariate as well as multivariate data. This allows robust modeling of high-dimensional multimodal and asymmetric data generated by popular biotechnological platforms such as flow cytometry. We develop Bayesian inference based on data augmentation and Markov chain Monte Carlo (MCMC) sampling. In addition to the latent allocations, data augmentation is based on a stochastic representation of the skew-normal distribution in terms of a random-effects model with truncated normal random effects. For finite mixtures of skew normals, this leads to a Gibbs sampling scheme that draws from standard densities only. This MCMC scheme is extended to mixtures of skew-t distributions based on representing the skew-t distribution as a scale mixture of skew normals. As an important application of our new method, we demonstrate how it provides a new computational framework for automated analysis of high-dimensional flow cytometric data. Using multivariate skew-normal and skew-t mixture models, we could model non-Gaussian cell populations rigorously and directly without transformation or projection to lower dimensions.

In the framework of Bayesian model-based clustering based on a finite mixture of Gaussian distributions, we present a joint approach to estimate the number of mixture components and identify cluster-relevant variables simultaneously as well as to obtain an identified model. Our approach consists in specifying sparse hierarchical priors on the mixture weights and component means. In a deliberately overfitting mixture model the sparse prior on the weights empties superfluous components during MCMC. A straightforward estimator for the true number of components is given by the most frequent number of non-empty components visited during MCMC sampling. Specifying a shrinkage prior, namely the normal gamma prior, on the component means leads to improved parameter estimates as well as identification of cluster-relevant variables. After estimating the mixture model using MCMC methods based on data augmentation and Gibbs sampling, an identified model is obtained by relabeling the MCMC output in the point process representation of the draws. This is performed using \(K\)-centroids cluster analysis based on the Mahalanobis distance. We evaluate our proposed strategy in a simulation setup with artificial data and by applying it to benchmark data sets.

We propose to pool multiple time series into several groups using finite-mixture models. Within each group, the same econometric model holds. We estimate the groups of time series simultaneously wi...