Selected topics in Statistics & Econometrics (Bayesian Methods and Hidden Markov Models)

Content

The lecture consists of two independent, equally weighted parts.

Part 1: Bayesian Methods
The Bayesian approach to statistical analysis is a natural way of combining prior information with empirical data, unlike the classical statistical analysis which is based solely on the theory of sampling. Recent advances in computing power and the development of simulation methods have increased the range of application of Bayesian methods and thus led to an increased popularity of these methods.

The first part of this course gives an introduction to the basic concepts of the Baysian approach and compares it to the classical approach. Monte Carlo Markov Chain (MCMC) methods, such as Gibbs sampling and the Metropolis-Hastings algorithm, which are used for the implementation of Bayesian methods, are also introduced. Finally, the topics of model diagnostics and model selection are covered.

Part 2: Hidden Markov Models
Hidden Markov models (HMMs) are a class of models in which the distribution that generates an observation depends on the state of an underlying and unobserved Markov process. They show promise as flexible general-purpose models for univariate and multivariate time series, especially for discrete-valued series, including categorical series and series of counts.

The second part of the course gives an introduction to hidden Markov Models. The emphasis will be on the application of the models, in particular model specification, parameter estimation, model selection, diagnostic checking, and forecasting.

There will be regular sessions in the computer lab in which students will be required to apply the methodology to real time series data. It is assumed that participants are familiar with the freeware statistical package R.