Bayesian Statistics and Credibility Theory

Name: Bayesian Statistics and Credibility Theory
Rating: 4.3 (90 reviews)

By MJ the Fellow Actuary

Last updated 5/2020

English

What you'll learn

1 section • 11 lectures • 49m total length

Visual Recap of Conditional Probability1:50
Bayesian Statistics Example5:00
Prior and Posterior Distributions2:31
Notation3:40
Prior and Posterior Example7:48
Conjugate Priors3:00
Loss Functions2:29
Credibility Theory4:26
Explore credibility theory and its connection to bayesian statistics in setting premiums by weighting the sample mean and population mean with the credibility factor Z.
Bayesian Credibility7:17
Empirical Bayes Credibility Theory4:47
Explore empirical Bayes credibility theory, comparing Model 1 with equal weights and Model 2 weighted by business volume, and focus on functions of the parameter rather than distributions.
Exam Question on EBCT6:46

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.