A Bayesian approach to the selection and testing of mixture models
نویسندگان
چکیده
An important aspect of mixture modeling concerns the selection of the number of mixture components. In this paper, we discuss the Bayes factor as a selection tool. The discussion will focus on two aspects: (i) computation of the Bayes factor and (ii) prior sensitivity. For the computation, we propose a variant of Chib’s estimator that accounts for the non-identifiability of the mixture components. To reduce the prior sensitivity of the Bayes factor, we propose to extend the model with a hyperprior. We further discuss the use of posterior predictive checks for examining the fit of the model. The ideas are illustrated by means of a psychiatric diagnosis example.
منابع مشابه
The Family of Scale-Mixture of Skew-Normal Distributions and Its Application in Bayesian Nonlinear Regression Models
In previous studies on fitting non-linear regression models with the symmetric structure the normality is usually assumed in the analysis of data. This choice may be inappropriate when the distribution of residual terms is asymmetric. Recently, the family of scale-mixture of skew-normal distributions is the main concern of many researchers. This family includes several skewed and heavy-tailed d...
متن کاملTesting Several Rival Models Using the Extension of Vuong\'s Test and Quasi Clustering
The two main goals in model selection are firstly introducing an approach to test homogeneity of several rival models and secondly selecting a set of reasonable models or estimating the best rival model to the true one. In this paper we extend Vuong's method for several models to cluster them. Based on the working paper of Katayama $(2008)$, we propose an approach to test whether rival models h...
متن کاملSpeech Enhancement Using Gaussian Mixture Models, Explicit Bayesian Estimation and Wiener Filtering
Gaussian Mixture Models (GMMs) of power spectral densities of speech and noise are used with explicit Bayesian estimations in Wiener filtering of noisy speech. No assumption is made on the nature or stationarity of the noise. No voice activity detection (VAD) or any other means is employed to estimate the input SNR. The GMM mean vectors are used to form sets of over-determined system of equatio...
متن کاملBayesian Sample size Determination for Longitudinal Studies with Continuous Response using Marginal Models
Introduction Longitudinal study designs are common in a lot of scientific researches, especially in medical, social and economic sciences. The reason is that longitudinal studies allow researchers to measure changes of each individual over time and often have higher statistical power than cross-sectional studies. Choosing an appropriate sample size is a crucial step in a successful study. A st...
متن کاملA One-Stage Two-Machine Replacement Strategy Based on the Bayesian Inference Method
In this research, we consider an application of the Bayesian Inferences in machine replacement problem. The application is concerned with the time to replace two machines producing a specific product; each machine doing a special operation on the product when there are manufacturing defects because of failures. A common practice for this kind of problem is to fit a single distribution to the co...
متن کاملModel Selection for Mixture Models Using Perfect Sample
We have considered a perfect sample method for model selection of finite mixture models with either known (fixed) or unknown number of components which can be applied in the most general setting with assumptions on the relation between the rival models and the true distribution. It is, both, one or neither to be well-specified or mis-specified, they may be nested or non-nested. We consider mixt...
متن کامل