Abstract
The Bayesian approach, which allows effective use of prior information, is especially useful in the situation that the sample evidence is insufficient. Researchers have used different probability distribution functions to express the prior distributions and the likelihood functions in various Bayesian inference models. However, little research has been done to examine the nature of different problems and thus select suitable likelihood functions. To respond to this research need, we proposed a Bayesian inference framework. For demonstration, we showed that, when a specific event (e.g., accident of failure) in a system occurs as a binomial process or Poisson process, the Bayesian inference model on the event rate will have the likelihood function as a binomial distribution or Poisson distribution, respectively.