Nonparametric Bayesian Statistics (WONDER)
||8 credit points
||Kleijn, B.J.K. (Universiteit van Amsterdam), Vaart, A.W. van der (Vrije Universiteit), van Zanten , J.H. (Universiteit van Amsterdam)
||firstname.lastname@example.org, email@example.com, firstname.lastname@example.org
||Introduction to the theory and a little practice of Bayesian
statistics for parameters in function spaces.
||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.
||Lectures. Home work exercises.
||To be determined.
||Lecture notes and parts of forthcoming book. These will be provided via a website.
||Probability theory, some knowledge of statistics.
Measure-theoretic probability and asymptotic statistics are recommended.
||*This is a course offered by WONDER. It is an advanced master and beginning graduate student level course. Students cannot apply for travel costs for this course