Bayesian Statistics and Credibility Theory
- Must have done a first year course in Mathematical Statistics in order to follow along.
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.
Who this course is for:
- Students wanting to writing the Actuarial Exams
Hi I'm MJ the Fellow Actuary. I've been making educational videos since 2013 on YouTube. I've passed all the actuarial exams and am here to help you do the same. I've majored in Mathematical Statistics and have published research in the South African Journal of Science on Artificial Intelligence. I've also done a Ted Talk on advanced studying methods. As your instructor my purpose is to make sure you understand every concept in these courses. If you get stuck with anything, send me a message, I'm here to help.