Logistic and Poisson regression, ordinal and multinomial logit models. Introduction to non-linear, log-linear and generalized linear models. Introduction to the general theory of linear models, least squares and maximum likelihood estimation. The topics covered include introduction to statistical computing, computer arithmetic, numerical linear algebra, regression computations, eigenproblems, numerical optimization, numerical approximations, numerical integration, expectation-maximization (EM) algorithm, basic simulation methodology, Monte Carlo (MC) integration, MC Markov Chain (MCMC) methods. This course introduces a range of computational techniques that are important to Statistics. STAT 556 Advanced Computing Method in Statistics STAT 555 Advanced Computational Statisticsīivariate and multivariate smoothing, discovering structure in data, nonparametric regression, Markov Chain Monte Carlo (MCMC), statistical pattern recognition: classifiers and clustering. Overview of statistical distributions, generating random variables, exploratory data analysis, Monte Carlo (MC) method for statistical inference, data partitioning, resampling, bootstrapping, nonparametric density estimation. STAT 553 Actuarial Analysis and Risk Theoryīasics of insurance Basics of reinsurance Non-life insurance mathematics Insurance economics Risk theory Individual and collective risk models Ruin theory Credibility theory and applications. Order statistics, exponential families, sufficiency, point estimation, hypothesis testing, interval estimation, confidence intervals. Probability, combinatorics, random variables, expectations, joint distribution functions, conditional distributions, distribution functions, moment generating functions, limit theorems. Simultaneous inference, multiple comparison procedures. Confidence, prediction and tolerance intervals. General regression models, residual analysis, selection of regression models, response surface methods, nonlinear regression models, experimental design and analysis of covariance models. Factorial design: confounding, aliasing, fractional replication. Construction and analysis of balanced and partially balanced complete and incomplete block designs. General analysis of experimental design models. Randomization theory of experimental design. STAT 518 Statistical Analysis of Designed Experiments Prerequisite: Advanced Calculus, Probabilitiy Theory. Weakly and strongly stationary processes, spectral analysis. Renewal processes, martingales, Brownian motion, branching processes. Markov chains, discrete and continuous Markov processes and associated limit theorems. General randomization theory of simple and multistage sampling, sampling with and without replacement and with equal and unequal probabilities, ratio and regression estimates, analytical studies and multiframe problems in relation to stratification, systematic sampling, clustering and double sampling. Relative efficiency, asymptotic relative efficiency and normal-score procedures. Use of order statistics and other distribution-free statistics for estimation and hypothesis testing, exact non-parametric tests and measures of rank correlation. STAT 504 Nonparametric Statistical Inference and Methods Likelihood theory, sufficiency, point estimation, methods of estimation, unbiasedness, Delta method, hypothesis testing, interval estimation, asymptotic theory, Bayesian statistics, loss function, inference for bivariate distributions. Probability, random variables, expectations, joint distribution functions, conditional distributions, distribution functions, moment generating functions, order statistics, censoring, limit theorems, multivariate normal distribution. (Open to the students of the Archaeometry Program). Elementary probability distributions, hypothesis testing, analysis of variance, analysis of frequencies with emphasis on the use of computers in processing data. Subjects covering statistical methodology in collecting band analyzing data. STAT 500 Statistical Methodology in Archaeometry
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