Bayesian Statistics and Credibility Theory

This short course aims to address the following syllabus objectives of the Actuarial Exams:Explain the fundamental concepts of Bayesian statistics and use these concepts to calculate Bayesian estimators. Use Bayes' theorem to calculate simple conditional probabilities. Explain what is meant by a prior distribution, a posterior distribution and a conjugate prior distribution.

Derive the posterior distribution for a parameter in simple cases. Explain what is meant by a loss function. Use simple loss functions to derive Bayesian estimates of parameters.

Explain what is meant by the credibility premium formula and describe the role played by the credibility factor. Explain the Bayesian approach to credibility theory and use it to derive credibility premiums in simple cases. Explain the empirical Bayes approach to credibility theory and use it to derive credibility premiums in simple cases.

Explain the differences between the two approaches and state the assumptions underlying each of them.