Topics covered for Statistics 610, spring 2010:

Overview and basics of inference: data (structure, context, randomness),
	probability models (parameterization, identifiability, parameter),
	confidence sets, hypothesis tests, point estimation, coverage 
	probability, decision rule, significance level, power, duality
	between tests and confidence sets, sampling distribution of 
	estimators (bias, variance, mean-squared error), consistency,
	confidence intervals based on asymptotic normality, delta method,
	measures of dependence (correlation, odds ratio, distance covariance),
	basic nonparametrics: empirical distribution, empirical process, 
	bootstrap (proof for percentile method) 
 
Parametric modeling: likelihood, maximum likelihood estimation, 
	score function, computational issues, Newton-like methods,  
	Jensen's inequality and EM algorithm, 
	sampling properties of MLE, consistency [iid sampling, finite
	parameter space], asymptotic normality [iid sampling, one parameter]
	Fisher information, Cauchy Schwartz inequality and the Cramer-Rao
	lower bound (with and without nuisance parameters), sufficient
	statistics, Rao-Blackwell method, factorization theorem (discrete case)
    
Testing revisited: Neyman Pearson lemma, uniformly most powerful tests,
	generalized likelihood ratio test, Wilks' theorem (one parameter),
	p-values,   GLR in normal models and contingency tables,
	exact conditional tests (Fisher's exact, and others),
	Wilcoxon rank sum test

Bayesian analysis: expanded interpretation of probability, 
	exchangeability, de Finetti's theorem (stated), Polya urn, 
	technique in one-parameter models, posterior expected loss, 
	highest posterior density regions, Bayes factors