This course covers mathematical statistics and probability. The emphasis will be on deepening your understanding of statistical theory. The topics covered include: Probabilistic models (for example: exponential families, gamma distributions) goodness of fit tests, discrete and continuous random variables, expectation, variance and covariance, data reduction and summarization, Bayes theorem and estimators, marginals, conditionals and independence, statistical determination of models (with linear regression, least squares and maximum likelihood), the Best Linear Unbiased Estimator (BLUE), hypothesis testing and needed tests (likelihood ratio tests, Chi-squared tests, Wald tests, multiple hypothesis tests, intersection-union tests, permutation tests), probability inequalities and convergence of random variables, delta methods, acceptance sampling, Poisson recursion, empirical distribution functions, negative binomials, confidence intervals, point estimates, confidence sets, method of moments, factorization theorem, order statistics, bootstrap methods, parametric inference, Bayesian inference and logistic regression. This course is a rigorous treatment of statistics that lays the foundation for EN.625.726 and other advanced courses in statistics.
Multivariate calculus and EN.625.603 Statistical Methods and Data Analysis or equivalent. An ability to read and understand mathematical proofs would be useful.