Special Topics in Statistics and Probability (STSP): Decision Theory

Basic concepts, classical risk and Bayes risk, decisions based on classical statistical principles, randomized rules, utility and loss, elements of utility theory, loss function, standard loss functions, Bayesian statistics, prior distribution, non-informative prior distributions, posterior distribution, conjugate families, the conjugate model of normal - inverse Gamma distribution, inference, estimation, credible intervals, Bayesian decision theory, posterior decisions, Bayes estimators, Bayesian hypothesis testing, simple null hypothesis testing, selection between two competing models.

Bibliography

• P. Papastamoulis, Elements of Decision Theory, Notes, 2019.
• J. O. Berger, Statistical Decision Theory and Bayesian Analysis, Springer, 1985