# Nonparametric Bayesian Statistics

A Bayesian statistical procedure consists of specifiying a prior probability distribution for the unknown parameter, viewing the likelihood of the statistical model as giving the conditional distribution of the data given the parameter, and next updating the prior distribution to the conditional distribution of the parameter given the data, i.e. the posterior distribution. In this course we shall be interested in the 'nonparametric' situation that the parameter is (possibly) a function, or another infinite-dimensional object. Then both prior and posterior are probabiity distributions on a function space. One example of a prior is the distribution of a stochastic process, for instance a Dirichlet or Gaussian process. We shall study examples of prior distributions (their definition, existence and some properties), and study the properties of the resulting posterior distributions. For the latter we adopt the 'frequentist framework', in which it is assumed that the data are generated according to a given parameter, and are usually concerned with the question whether the posterior is able to reconstruct this parameter, for instance if the amount of data would increase indefinitely.

## Course spring 2012

 Lecture hour Thursdays 14.00-16.45, starting September 6. Lecture room Buys Ballot Lab, room BBL 169, Utrecht Office hour On appointment. Registration Via mastermath. Lecturers Bas Kleijn, Aad van der Vaart. , Harry van Zanten Exam To be determined. Retake Exam To be determined. Grades Grades will be communicated to the mastermath administration, and can be obtained on request by sending an email to the lecturer, approximately two weeks after the exam. Credits 8. Lecture Notes

## Course schedule (may be adapted during the semester)

The lecture notes BNP.pdf will grow during the semester, and earlier parts may be corrected or changed without warning. So it is a good idea to print a fresh version at the end of the semester.
The listed exercises are suggestions. A good time to try would be after studying the week's material. A selection of exercises is discussed in the final lecture hour. You can make your own wish list for this selection!

 Week Subject Exercises 6 September Intro (slides until Gaussian process priors), BNP.pdf, pages 1-12 2.1, 2.2 13 September BNP.pdf, pages 13-21 3.1, 3.2, 3.3, 3.5, 4.1 20 September BNP.pdf, pages 23-30 4.4, 4.5, 5.1, 5.2 27 September BNP.pdf, pages 31-33, 37, 39-40 6.2, 6.3, 7.1, 7.2 4 October BNP.pdf, pages 41-42, 44-47