Asian Journal of Probability and Statistics

This paper presents Bayesian analysis of Seemingly Unrelated Regression (SUR) model. An independent prior for parameters was used. The Bayesian method was compared with classical method of estimation to know the most efficient estimator under different distributional assumptions through a simulation study. In order to facilitate comparison among these estimators, Mean Squared Error (MSE) was considered as a criterion. Furthermore, based on the simulation, it was deduced that MSE of the Bayesian estimator is smaller than all the classical methods of estimation for SUR model while Normal distribution was considered as an ideal distribution  in generation of disturbances in any simulation study.

In the present research work, two probabilistic models are constructed, which are exponential regression and negative binomial regression. The first one refers to the number of positive cases of being infected by COVID-19. The second one refers to deaths. It was possible to estimate the dynamics of the phenomenon with both instruments, resulting in the presence of more than 106 thousand positive cases of COVID - 19, with an approximation of more than 9 thousand deaths, all of this, in approximately 4 months. In the first case, these were the results, which when updated with data issued by the federal government's health sector in November, changed the contagion scenarios and the estimates of deaths from covid-19.

Aims/ objectives: To develop a state-transition model for malaria symptoms. Study design: Longitudinal study. 

Place and Duration of Study: Department of Mathematics Masinde Muliro University of Science and Technology between January 2015 and December 2015. 

Methodology: We included 300 students (patients) with liver malaria disease, with or without the medical history of malaria disease, physical examination for signs and symptoms for both specific and non-specific symptom, investigation of the disease through laboratory test (BS test) and diagnostic test results. the focus of this study was to develop state-transition model for malaria symptoms. Bayesian method using Markov Chain Monte Carlo via Gibbs sampling algorithm was implemented for obtaining the parameter estimates. 

Results: The results of the study showed a significant association between malaria disease and observed symptoms 

Conclusion: The study findings provides a useful information that can be used for predicting malaria disease in areas where Blood slide test and rapid diagnostic test for malaria disease is not possible.

Box and Hunter (1957) introduced the concept of rotatability. It is an important design criterion for response surface methodology (RSM). In this paper, evaluating measure of modified rotatability for second degree polynomial design using balanced incomplete block designs (3 ≤ V ≤ 11 : v-number of factors) which enables us to assess the degree of modified rotatability for a given response surface designs at different values of rotatability is recommended.

Overtime finite mixtures of Normal in regression have gained popularity and also shown to be useful in modelling heterogeneous data. This study examines the effects of prior and sample size in regression mixtures of Normal models with Bayesian approach. Monte Carlo experiment was carried out on the Normal mixtures model in order to examine the strength of priors and also to know the suitable sample size to produce stable results. Results obtained from the experiment indicate that an informative prior gives a reliable estimate than non-informative prior while large sample sizes maybe needed to obtain stable results.