Mixture and Non-Mixture Bayesian Hierarchical Study of Seizure Count Data Using New Generalized Poisson Model

Jamal A. Al-saleh, Satish K. Agarwal

Abstract


In this paper Bayesian methods is performed on a medical trial Seizure count data set by introducing the new three parameter generalized Poisson model GPM(α,β,l) as an alternative model to the standard Poisson model SPM(l) which is considered on an earlier work for the generalized linear mixed model. The new model is developed by introducing two more parameters α and β called indicator parameters. The main advantage of an indicator parameter is that it gives the new Poisson model the mixture (when α>0,β=1,2) and non-mixture (when α=0) options. Another feature of proposed new model is that it generalize the posterior of the parameters to predict the behavior of the Seizure counts data, in agreement with generalized linear mixed model. Unlike earlier authors, who confined and limited their work only on standard Poisson model SPM(l), to analyze the counts data in generalized linear mixed model, which make the new model more resilience and litheness. The parameters of the new model will be estimated using Bayesian approach that serves as a subtle tool for model selection and identification. An illustration is provided using the Seizure count data. The posterior summaries using Markov Chain Monte Carlo (MCMC) Gibbs sampling approach are presented for the new model for different values of the parameters. The study of the estimated parameters would help the users to have more prospect and clarity about the role of the new model. It is found that using proposed new model in generalized linear mixed model has more resiliency than standard Poisson model considered earlier. The proposed model is fully adaptive to the available data and gives scientists another option for modeling the data.


Keywords


Bayesian predictions; generalized Poisson model; generalized posterior; Gibbs sampling; Hierarchical model; Markov Chain Monte Carlo.

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