Bivariate pseudo modeling

Abstract

Abstract newlineThe existence of normal marginals and normal conditionals in the traditional bivariate newlinenormal distributions is widely known. It makes it natural to wonder if Poisson newlinemarginals and conditionals can experience a similar phenomenon. However, it is known newlinefrom studies on conditionally specified models that Poisson marginals and both conditionals newlinewould only be seen in the scenario when the variables are independent. This newlinethesis discusses a bivariate pseudo-Poisson model in which the conditional density newlineof one variable and the marginal density of the other are both Poisson forms. These newlinemodels are commonly used to model bivariate count data with a positive correlation. newlineMoreover, such models have simple, flexible dependence structures and generate a newlinesufficiently large number of parametric families. It has been a strong case made for newlinethe pseudo-Poisson model as the initial option to take into account when modeling bivariate newlineover-dispersed data with positive correlation and having one of the marginal newlineequi-dispersion. In the current thesis, we look at separate gamma priors for the parameters newlineas well as pseudo-gamma priors for the Bayesian estimation of the unknown newlineparameters of bivariate pseudo-Poisson models. Both comprehensive and sub-model newlineinvestigations of potential conjugacy are verified, and conjugate priors can be found in newlinesome unique sub-instances. The effectiveness of Bayesian parameter estimates employing newlinea range of priors, both informative and non-informative, is demonstrated through newlinea simulation study. Two well-known bivariate count data sets are re-analyzed to illustrate newlinethe methodologies. Similarly, we also considered a bivariate pseudo-exponential newlinemodel initially introduced by Arnold and Arvanitis (2019) for Bayesian analysis using newlinepseudo gamma priors and independent gamma priors for the parameters. We also newlineinclude an application to the Infant mortality and GDP data set. newlinexiii newlineYet, before we start fitting, it is necessary to test whether the given data is compatible newlinewith the assumed pseudo-Poisson mode