41505 - Bayesian Statistical Inference

Academic Year 2017/2018

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)

    Also valid for Second cycle degree programme (LM) in Statistical Sciences (cod. 8875)

Learning outcomes

At the end of the course the students knows the basis of Bayesian inference and possesses the tools for addressing the problems of parametric estimate, predictive inference and hypothesis testing according to the Bayesian viewpoint. In particular, the student is able to face the problems above and to use statistica software for estimating Bayesian models.

Course contents

Comparison between classical and Bayesian framework.

Bayes theorem for events and random variables. Revision of a prior via an experiment.

Bayes inference for events with discrete priors. Odds ratios for couples of events.

Open problems in the classical statistical models.

Posterior and predictive distributions for a Bernoulli likelihood and discrete and continuous prior distribution. The Beta distribution. Bayesian inference for the normal-normal case with known variance.

Sufficient statistics in Bayesian inference. Natural conjugate distributions.

One parameter exponential family.

Gamma Poisson model,

Gamma and Chi-square distribution.

Inference on the variance of the normal model with known mean.

Inference on the precision of the normal model with known mean.

Two parameters exponential family.

Non informative priors, reference priors.

Alternative formulation for the ignorance on the parameter of the Binomial distribution. Improper priors and Jeffrey's rule. Parameterization of the negative binomial distribution. Echangeability and hierarchical models. Interval estimation. Hypothesis testing.

Introduction to Winbugs.

Readings/Bibliography

Bibliographical references will be given at the beginning of the course

Teaching methods

The course is made of lectures and computer sessions

Assessment methods

The final test will consist of a computer session and an oral test. The computer session will occupy about two hours, will be organized in one of the computer rooms and will be mainly devoted to the construction of a model to solve and assess via the software WinBugs. The oral test is focused on the theory and technical points illustrated during the course.

Teaching tools

The course is completed with computer session introducing the WinBugs software

Office hours

See the website of Daniela Cocchi