Bayesian Panel Data Model Based on Markov Chain Monte Carlo

The general aim of this paper is to deal with problems of estimation , prediction, and model building for panel data model .Bayesian approach based on Markov chain Monte Carlo (MCMC) employed to make inferences on panel data model coefficients under some conditions on the prior distribution . We investigate the posterior density and identify the analytic form of the Bayes factor for checking the model.   Keywords: Panel Data Model , Likelihood function , Bayesian approach , Markov chain Monte Carlo (MCMC), Prior distribution, Posterior distribution , Bayes factor

A Note on Bayes Semiparametric Regression

In the Bayesian approach to inference, all unknown quantities contained in a probability model for the observed data are treated as random variables. Specifically, the fixed but unknown parameters are viewed as random variables under the Bayesian approach. In this paper, Bayesian approach is employed to making inferences on the semiparametric regression model as mixed model , and we prove some theorems about posterior. Keywords?Mixed models, Semiparametric regression, Penalized spline, Bayesian inference, Prior density, Posterior density

Some Remarks on Restricted Panel Data Model

In this paper , we investigate some remarks on panel data model with linear constraints on the coefficients of the random panel data model. Furthermore, it investigates the inferences . The restricted maximum likelihood method is employed to making inferences on the random panel data model

Large Sample Property of The Bayes Factor in a Spline Semiparametric Regression Model

In this paper, we consider semiparametric regression model where the mean function of this model has two part, the first is the parametric part is assumed to be linear function of p-dimensional covariates and nonparametric ( second part ) is assumed to be a smooth penalized spline. By using a convenient connection between penalized splines and mixed models, we can representation semiparametric regression model as mixed model. In this model, we investigate the large sample property of the Bayes factor for testing the polynomial component of spline model against the fully spline semiparametric alternative model. Under some conditions on the prior and design matrix, we identify the analytic form of the Bayes factor and show that the Bayes factor is consistent. Keywords: Mixed Models, Semiparametric Regression Model, Penalized Spline, Bayesian Model, , Marginal Distribution, Prior Distribution, Posterior Distribution, Bayes Factor,  Consistent

Bayesian One- Way Repeated Measurements Model as a Mixed Model

In the Bayesian approach to inference, all unknown quantities contained in a probability model for the observed data are treated as random variables. Specifically, the fixed but unknown parameters are viewed as random variables under the Bayesian approach. In this paper, Bayesian approach is employed to making inferences on the one- way repeated measurements model as mixed model , and we prove some theorems about posterior. Keywords: Mixed models, One- way repeated measurements model , Bayesian inference, Prior density, Posterior density

Asymptotic Properties of Bayes Factor in One- Way Repeated Measurements Model

In this paper, we consider the linear one- way repeated measurements model which has only one within units factor and one between units factor incorporating univariate random effects as well as the experimental error term. In this model, we investigate the consistency property of Bayes factor for testing the fixed effects linear one- way repeated measurements model against the mixed one- way repeated measurements alternative model. Under some conditions on the prior and design matrix, we identify the analytic form of the Bayes factor and show that the Bayes factor is consistent. Keywords:  One- Way Repeated Measurements Model, ANOVA, Mixed model, Prior Distribution, Posterior Distribution, covariance matrix, Bayes Factor, Consistent.

Bayesian One- Way Repeated Measurements Model Based on Bayes Quadratic Unbiased Estimator

In this paper, bayesian approach based on Bayes quadratic unbiased estimator is employed to the linear one- way repeated measurements model which has only one within units factor and one between units factor incorporating univariate random effects as well as the experimental error term. The prior information obtained by using variance analysis technique to represent prior estimates of the parameters of the model. Then, the prior distribution is considered as a uniform distribution

A note on Bayesian One-Way Repeated Measurements Model

In this paper, we consider the linear one- way repeated measurements model which has only one within units factor and one between units factor incorporating univariate random effects as well as the experimental error term. Bayesian approach based on Markov Chain Monte Carlo is employed to making inferences on the one- way repeated measurements  model.   Keywords: Repeated Measurements, ANOVA, Bayesian inference, Prior density, posterior density, Bayes factor

Spline Semiparametric Regression Models

In this paper, we study semiparametric regression models with spline smoothing, and determining the numbers of knots and their locations by using some statistical criteria, a simulation model has been performed