Statistical Inference

Abstract

Joint, conditional, and marginal distributions for data and parameters, prior distribution, posterior distribution, likelihood function, loss functions, decision-theoretic approach to inference, frequentist risk, minimax estimators, admissible estimators, posterior expected loss, integrated risk, Bayes risk, calculating Bayes estimators, generalized Bayes estimators, improper prior distributions, maximum likelihood estimators, least squares estimators. Neyman-Pearson tests, null hypothesis, alternative hypothesis, point hypothesis, composite hypothesis, type-I error, type-II error, power, uniformly most powerful tests, Neyman-Pearson lemma, likelihood ratio test, frequentist confidence intervals via inversion of test statistics, Bayesian credible sets.