Model selection and hypothesis testing problems in Bayesian inference are still debated between scholars. Bayesian factors traditionally used as a criterion in Bayesian hypothesis testing and model selection, are easy to understand but sometimes hard to compute. In addition, there are other model selection criterions such as DIC(Deviance Information Criterion) by Spiegelhalter et al. (2002) and Bayesian P-values for testing. In this paper, we briefly introduce the Bayesian hypothesis testing and model selection procedure. In addition we have applied a Bayesian inference to Swiss banknote data by a fitting logistic regression model and computing several test statistics to see if they provide consistent results.