The Comparison between Results of Application Bayesian and Maximum Likelihood Approaches on Logistic Regression Model for prostate cancer Data

The logistic regression model is one of the statistical models that widely used to analyze binary response data. Bayesian and maximum likelihood methods were used to model binary data for prostate cancer. In Bayesian method Gibbs sampling algorithm was used to select 5 millions samples from posterior distribution of logistic coefficients under flat non-informative prior. Then mean, standard deviation, and some percentiles of posterior distribution were computed. The empirical results showed that the estimates of coefficients and mean square errors for Bayesian approach not different from maximum likelihood approach, but the percentage of correct classification when using Bayesian approach greater little than maximum likelihood. Also in the testing lack of fit, the probability of accept the null hypotheses that model is appropriate under Bayesian approach greater little than the probability of accept the null hypotheses under maximum likelihood approach. The research recommended using Bayesian approach for making statistical inference about application of the logistic regression model on prostate cancer data because Bayesian approach allows for probabilistic interpretations to logistic coefficients and its results more accurate than the maximum likelihood method at least the same accuracy under non-informative prior. Keyword: Binary logistic model, Bayesian inference, Gibbs sampling, Maximum likelihood Estimates (MLE), Bayes factor 1144 N. I. Rashwan and M. El dereny