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The traditional Poisson regression model for fitting count data is considered inadequate to fit over-or under-dispersed count data and new models have been developed to make up for such inadequacies inherent in the model. In this study, Bayesian Multi-level model was proposed using the No-U-Turn Sampler (NUTS) sampler to sample from the posterior distribution. A simulation was carried out for both over-and under-dispersed data from discrete Weibull distribution. Pareto k diagnostics was implemented, and the result showed that under-dispersed and over-dispersed simulated data has all its k value to be less than 0.5, which indicate that all the observations are good. Also all WAIC were the same as LOO-IC except for Poisson in the over-dispersed simulated data. Real-life data set from National Health Insurance Scheme (NHIS) was used for further analysis. Seven multi-level models were f itted and the Geometric model outperformed other model.

The emergence of global pandemic known as COVID-19 has impacted significantly on human lives and measures have been taken by government all over the world to minimize the rate of spread of the virus, one of which is by enforcing lockdown. In this study, Autoregressive fractionally integrated moving average (ARFIMA) Models was used to model and forecast what the daily new cases of COVID-19 would have been ten days after the lockdown was eased in Nigeria and compare to the actual new cases for the period when the lockdown was eased. The proposed model ARFIMA model was compared with ARIMA (1, 0, 0), and ARIMA (1, 0, 1) and found to outperform the classical ARIMA models based on AIC and BIC values. The results show that the rate of spread of COVID-19 would have been significantly less if the strict lockdown had continued. ARFIMA model was further used to model what new cases of COVID-19 would be ten days ahead starting from 31st of August 2020. Therefore, this study recommends that government should further enforce measures to reduce the spread of the virus if business must continue as usual.

This study aim at optimizing the parameter θ of Discrete Weibull (DW) regression obtained by maximizing the likelihood function. Also to examine the strength of three acquisition functions used in solving auxiliary optimization problem. The choice of Discrete Weibull regression model among other models for fitting count data is due to its robustness in fitting count data. Count data of hypertensive patients visits to the doctor was obtained at Medicare Clinics Ota, Nigeria, and was used for the analysis. First, parameter θ and β were obtained using Metropolis Hasting Monte Carlo Markov Chain (MCMC) algorithm. Then Bayesian optimization was used to optimize the parameter the likelihood function of DW regression, given β to examine what θ would be, and making the likelihood function of DW the objective function. Upper confidence bound (UCB), Expectation of Improvement (EI), and probability of Improvement (PI) were used as acquisition functions. Results showed that fitting Bayesian DW regression to the data, there is significant relationship between the response variable, β and the covariate. On implementing Bayesian optimization to obtain parameter new parameter θ of discrete Weibull regression using the known β, the results showed promising applicability of the technique to the model, and found that EI fits the data better relative to PI and UCB in terms of accuracy and speed.

The need to model count data correctly calls for introducting a flexible yet robust model that can sufficiently handle various types of count data. Models such as Ordinary Least Squares (OLS) used in the past were considered unsuitable. The introduction of the Generalized Linear Model (GLM) and its various extensions was the first breakthrough recorded in modeling count data. Thishis article, propose the Bayesian Dirichlet process mixture prior of generalized linear mixed models (DPMglmm). Metropolis Hasting Monte Carlo Markov Chain (M-H MCMC) was used to draw parameters from target posterior distribution. The Iterated Weighted Least Square (IWLS) proposal was used to determine the acceptance probability in the M-H MCMC phase. Under and over-dispersed count data were simulated, 500 Burn-in was scanned to allow for stability in the chain. 100 thinning interval was allowed so as to nullify the possible effect of autocorrelation in the data due to the Monte Carlo procedure. The DPMglmm and other competing models were fitted to the simulated data, and real-life health insurance claims data sets. The results obtained showed that DPMglmm outperformed MCMCglmm, Bayesian Discrete Weibull, and four other frequentist models. This indicates that DPMglmm is flexible and can fit count data best, either under-dispersed or over-dispersed data.

It is important to fit count data with suitable model(s), models such as Poisson Regression, Quassi Poisson, Negative Binomial, to mention but a few have been adopted by researchers to fit zero truncated count data in the past. In recent times, dedicated models for fitting zero truncated count data have been developed, and they are considered sufficient. This study proposed Bayesian multi-level Poisson and Bayesian multi-level Geometric model, Bayesian Monte Carlo Markov Chain Generalized linear Mixed Models (MCMCglmms) of zero truncated Poisson and MCMCglmms Poisson regression model to fit health count data that is truncated at zero. Suitable model selection criteria were used to determine preferred models for fitting zero truncated data. Results obtained showed that Bayesian multi-level Poisson outperformed Bayesian multi-level Poisson Geometric model; also MCMCglmms of zero truncated Poisson outperformed MCMCglmms Poisson.