41505 - Bayesian Statistical Inference

Learning outcomes

The main learning goal of the course is to familiarize students with the basis of Bayesian inference and the tools for parametric estimate and hypothesis testing according to the Bayesian viewpoint. In particular, a student will be able to use statistical software for modeling techniques in actuarial and financial applications.

Course contents

• Introduction to Bayesian inference: the likelihood principle; prior and posterior distributions.
• Summarizing posterior information.
• Inference about parameters of some standard univariate models.
• Relevance of Sufficient Statistics in Bayesian Inference. Conjugate priors.
• Non informative priors and and reference priors.
• Improper priors. The Jeffrey's rule.
• Interval estimation. Hypothesis testing.
• Introduction to Bayesian computational methods. Markov chain Monte Carlo methods.
• Loss functions and posterior expected loss.
• Hierarchical models.
• Introduction to WinBugs.
• Case studies in finance and insurance.

Readings/Bibliography

Lee P.M., Bayesian Statistics: an Introduction, Arnold, 2004.

Some additional readings will be found at http://www2.stat.unibo.it/trivisano/.

 

Teaching methods

Each topic covered in the lectures will be followed by exercises in practical classes.

Assessment methods

The final test will consist of a computer session and an oral test.

Office hours

See the website of Carlo Trivisano