Bayesian statistics

Subject description

Bayesian models with one and more parameters. Connection with standard statistical methods. Hierachical models. Testing of models and sensitivity analysis. Bayesian design of experiment.

Introduction to regression analysis. Analysis of variance and covariance. Hypothesis testing with Bayes factors, complexity and fit. Posterior probabilities of hypotheses – models, and influence of priors on them, training sample.

More on posterior probabilities, estimating parameters, central credibility interval, the importance of conjugated distributions. Gibbs sampler, convergence of estimates, Metropolis-Hastings algorithm. Posterior simulations. Some other specific models of Bayesian analysis.

The subject is taught in programs

Objectives and competences

Basic knowledge of Bayesian statistics and its application in data analysis is acquired.

Teaching and learning methods

Lectures, exercises, seminar type homework, homework that require the use of statistical packages, consultations

Part of the pedagogical process will be carried out with the help of ICT technologies and the opportunities they offer.

Expected study results

Understanding of basic concepts of Bayesian statistics.

Basic sources and literature

  • A. Gelman, J.B.Carlin, H.S. Stern, D.B. Rubin: Bayesian Data Analysis. Chapman&Hall, 1995.
  • H. Hoijtink: Bayesian Data Analysis. In: R.E. Millsap and A. Maydeu-Olivares, The SAGE Handbook of Quantitative Methods in Psychology. London: SAGE, 2009.
  • I. Ntzoufras: Bayesian Modeling Using WinBUGS. New York: Wiley, 2009.
  • P. Hoff: A First Course in Bayesian Statistical Methods, Springer Texts in Statistics, Springer, 2009.

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