Keeping the balance—Bridge sampling for marginal likelihood estimation in finite mixture, mixture of experts and Markov mixture models

Approximating the marginal likelihood in mixture models

In Chib (1995), a method for approximating marginal densities in a Bayesian setting is proposed, with one proeminent application being the estimation of the number of components in a normal mixture. As pointed out in Neal (1999) and Frühwirth-Schnatter (2004), the approximation often fails short of providing a proper approximation to the true marginal densities because of the well-known label s...

Likelihood inference in some finite mixture models

Parametric mixture models are commonly used in applied work, especially empirical economics, where these models are often employed to learn for example about the proportions of various types in a given population. This paper examines the inference question on the proportions (mixing probability) in a simple mixture model in the presence of nuisance parameters when sample size is large. It is we...

Penalized Likelihood Estimation in Gaussian Mixture Models

Empirical Likelihood Estimation of Censored Mixture Models

In this paper, a mixture model is estimated by the empirical likelihood (EL) approach. The functional delta method is implemented to exploit asymptotic properties of the estimator. EL constructs a weighted empirical process that converges to a Gaussian process and its estimator, with additional assumptions, converges a normal distribution with an asymptotic efficient covariance matrix. This app...

Marginal Likelihood and Bayes Factors for Dirichlet Process Mixture Models

We present a method for comparing semiparametric Bayesian models, constructed under the Dirichlet process mixture (DPM) framework, with alternative semiparameteric or parameteric Bayesian models. A distinctive feature of the method is that it can be applied to semiparametric models containing covariates and hierarchical prior structures, and is apparently the Ž rst method of its kind. Formally,...