Statistical Inference

H Migon, D Gamerman, Both at the University of Rio de Janerio, Brazil

Information; the concept of probability; linear algebra and probabilities; elements of inference; common statistical models; likelihood based functions; Bayes theorem; exchangeability; sufficiency and exponential family; parameter elimination; prior distribution; entirely subjective specification; specification through functional forms; conjugacy with the exponential family; the main conjugate families; non-informative priors; hierarchical priors; estimation; introduction to decision theory; classical point estimation; criterion of estimators; interval estimation; estimation in the normal model; approximate methods; general problem of inference; optimization techniques; analytical approximations; numerical integration methods; simulation methods; hypothesis testing; classical hypothesis testing; Bayesian hypothesis testing; hypothesis testing and confidence intervals; asymptotic tests; prediction; Bayesian prediction; classical prediction; prediction in the linear model; linear prediction; introduction to linear models; classical linear models; Bayesian linear models; hierarchical linear models; dynamic linear models.