Criteria of choice, and optimality consideration, in respect of point estimation, hypothesis tests and confidence intervals.  Likelihood methods with special consideration of maximum likelihood estimates (m.l.e.) and likelihood ratio tests including multiparameter problems (and linearisation methods).  Specific techniques will include:  Hypothesis Testing:

Pure significance tests, simulation tests, Neyman Pearson Lemma, UMP test.  Point Estimations: Efficiency, consistency, minimum variance bound estimators.  Determination of m.l.e’s including linearisation and asymptotic properties, maximum likelihood ratio tests and large-sample equivalents, asymptotic           optimality. Score tests.  Jackknifing, bootstrapping. Prior distributions: Representation of prior information via a prior distribution, substantial information, vague priors and ignorance, empirical Bayes ideas. Normal Models: Theory for  unknown), prior-posterior-predictive, normal regression model. Comparisons: Comparisons of classical, Bayesian, decision-theory approaches and conclusions via specific examples.