Bayesian analysis

Matrix-variate beta distributions are applied in different fields of hypothesis testing, multivariate correlation analysis, zero regression, canonical correlation analysis and etc. A methodology is proposed to generate matrix-variate beta generator distributions by combining the matrix-variate beta kernel with an unknown function of the trace operator. Several statistical characteristics, extensions and developments are presented. Special members are then used in a univariate and multivariate Bayesian analysis setting. These models are fitted to simulated and real datasets, and their fitting and performance are compared to well-established competitors.

A longitudinal study refers to collection of a response variable and possibly some explanatory variables at multiple follow-up times. In many clinical studies with longitudinal measurements, the response variable, for each patient is collected as long as an event of interest, which considered as clinical end point, occurs. Joint modeling of continuous longitudinal measurements and survival time is an approach for accounting association between two outcomes which frequently discussed in the literature, but design aspects of these models have been rarely considered. This paper uses a simulation-based method to determine the sample size from a Bayesian perspective. For this purpose, several Bayesian criteria for sample size determination are used, of which the most important one is the Bayesian power criterion (BPC), where the determined sample sizes are given based on BPC. We determine the sample size based on treatment effect on both outcomes (longitudinal measurements and survival time). The sample size determination is performed based on multiple hypotheses. Using several examples, the proposed Bayesian methods are illustrated and discussed. All the implementations are performed using R2OpenBUGS package and R 3.5.1 software.