Typically, in high dimensional data sets, many covariates are not significantly associated with a response. Moreover, those covariates are highly correlated, leading to a multicollinearity problem. Hence, the model is sparse since the coefficient of most covariates are likely to be zero. The classical frequentist or likelihood-based variable selection via any criterion such as Bayesian Information Criteria (BIC) and Akaike Information Criteria (AIC) or a stepwise subset selection becomes infeasible when the number of variables are large. An alternative solution is a Bayesian variable selection. In this study, we used a variable selection via a Bayesian variable selection and the least absolute shrinkage and selection operator (LASSO) method in the logistic regression model. Moreover, those methods were expanded to be applied to real datasets.

The discrete Weibull model can be adapted to capture different levels of dispersion in the count data. This paper takes into account the direct relationship between explanatory variables and the median of discrete Weibull response variable. Additionally, it provides the Bayesian estimate of the discrete Weibull regression model using the random walk Metropolis algorithm. The prior distributions of the coefficient predictors were carried out based on the uniform non-informative, normal and Laplace distributions. The performance of the Bayes estimators was also compared with the maximum likelihood estimator in terms of the mean square error and the coverage probability through the Monte Carlo simulation study. Meanwhile, a real data set was analyzed to show how the proposed model and the methods work in practice.