Bayesian Analysis of Finite Poisson Mixtures
نویسندگان
چکیده
Finite Poisson mixtures are widely used to model overdispersed data sets for which the simple Poisson distribution is inadequate. Such data sets are very common in real applications. In this paper we investigate Bayesian estimation via MCMC for finite Poisson mixtures and we discuss some computational issues. The related problem of determining the number of components in a mixture is also treated. This problem is of particular interest since it can reveal the number of subpopulations comprising the entire population under study. We model the number of components k as a random quantity having itself a prior probability function and then we apply the Reversible Jump Markov Chain Monte Carlo (Green 1995) to estimate the number of components. A real data example dealing with a financial credit scoring system illustrates our methodology.
منابع مشابه
Estimation of Products Final Price Using Bayesian Analysis Generalized Poisson Model and Artificial Neural Networks
Estimating the final price of products is of great importance. For manufacturing companies proposing a final price is only possible after the design process over. These companies propose an approximate initial price of the required products to the customers for which some of time and money is required. Here using the existing data of already designed transformers and utilizing the bayesian anal...
متن کاملBayesian paradigm for analysing count data in longitudina studies using Poisson-generalized log-gamma model
In analyzing longitudinal data with counted responses, normal distribution is usually used for distribution of the random efffects. However, in some applications random effects may not be normally distributed. Misspecification of this distribution may cause reduction of efficiency of estimators. In this paper, a generalized log-gamma distribution is used for the random effects which includes th...
متن کاملBayesian inference for transportation origin-destination matrices: the Poisson-inverse Gaussian and other Poisson mixtures
Transportation origin-destination analysis is investigated through the use of Poisson mixtures by introducing covariate-based models which incorporate different transport modelling phases and also allow for direct probabilistic inference on link traffic based on Bayesian predictions. Emphasis is placed on the Poisson-inverse Gaussian model as an alternative to the commonly used Poisson-gamma an...
متن کاملBayesian change point estimation in Poisson-based control charts
Precise identification of the time when a process has changed enables process engineers to search for a potential special cause more effectively. In this paper, we develop change point estimation methods for a Poisson process in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point where there exists a step < /div> change, a linear trend and a known multip...
متن کاملChoosing initial values for the EM algorithm for finite mixtures
The EM algorithm is the standard tool for maximum likelihood estimation in )nite mixture models. The main drawbacks of the EM algorithm are its slow convergence and the dependence of the solution on both the stopping criterion and the initial values used. The problems referring to slow convergence and the choice of a stopping criterion have been dealt with in literature and the present paper de...
متن کامل