A Partially Linear Model Using a Gaussian Process Prior

A partially linear model is a semiparametric regression model that consists of parametric and nonparametric regression components in an additive form. In this article, we propose a partially linear model using a Gaussian process regression approach and consider statistical inference of the proposed model. Based on the proposed model, the estimation procedure is described by posterior distributions of the unknown parameters and model comparisons between parametric representation and semi- and nonparametric representation are explored. Empirical analysis of the proposed model is performed with synthetic data and real data applications.     

A Bayesian Approach for Zero-Inflated Count Regression Models by Using the Reversible Jump Markov Chain Monte Carlo Method and an Application

In this study, estimation of the parameters of the zero-inflated count regression models and computations of posterior model probabilities of the log-linear models defined for each zero-inflated count regression models are investigated from the Bayesian point of view. In addition, determinations of the most suitable log-linear and regression models are investigated. It is known that zero-inflated count regression models cover zero-inflated Poisson, zero-inflated negative binomial, and zero-inflated generalized Poisson regression models. The classical approach has some problematic points but the Bayesian approach does not have similar flaws. This work points out the reasons for using the Bayesian approach. It also lists advantages and disadvantages of the classical and Bayesian approaches. As an application, a zoological data set, including structural and sampling zeros, is used in the presence of extra zeros. In this work, it is observed that fitting a zero-inflated negative binomial regression model creates no problems at all, even though it is known that fitting a zero-inflated negative binomial regression model is the most problematic procedure in the classical approach. Additionally, it is found that the best fitting model is the log-linear model under the negative binomial regression model, which does not include three-way interactions of factors.