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The systematic progression of statistical principles needed to conduct a statistical investigation culminating in parameter estimation, hypothesis testing, statistical modelling, and design of experiments. Course Hours:3 units; (3-1T) Prerequisite(s):One of Mathematics 30-1, 30-2, 212 or Mathematics 2 (offered by Continuing Education). Antirequisite(s):Credit for Statistics 205 and any one of Statistics 213, 217, or 327 will not be allowed. Students may not register in, or have credit for, Statistics 205 if they have previous credit for one of Statistics 321, Engineering 319 or Digital Engineering 319 or are concurrently enrolled in Statistics 321, Engineering 319 or Digital Engineering 319.

Introduction to Statistical Enquiry for Data Scientists

An introductory course in statistical literacy. Data collection methodology and import. Data properties trending to the probability modelling of data and computation with R. Relative risk and Odds Ratios. Statistical sampling theory applied to parameter estimation and the testing of statistical hypotheses. Testing of single and multi-populations. Regression and Design and analysis of experiments with R. Simulation based inference. Course Hours:3 units; (3-1T) Prerequisite(s):One of Mathematics 30-1, 30-2, 212 or Mathematics 2 (offered by Continuing Education). Antirequisite(s):Credit for Statistics 207 and any one of Statistics 205, 213, 217, or 327 will not be allowed. Students may not register in, or have credit for, Statistics 207 if they have previous credit for one of Statistics 321, Engineering 319 or Digital Engineering 319 or are concurrently enrolled in Statistics 321, Engineering 319 or Digital Engineering 319.

Introduction to probability, including Bayes' law, expectations and distributions. Discrete and continuous random variables, including properties of the normal curve. Collection and visual display of single and multi-dimensional data. Introduction to statistical modelling and estimation. Parametric and simulation-based confidence interval estimation. Course Hours:3 units; (3-1) Prerequisite(s):One of Mathematics 30-1, 212 or Mathematics 2 (offered by Continuing Education). Antirequisite(s):Credit for Statistics 213 and either Statistics 205 or 327 will not be allowed. Not available to students who have previous credit for one of Statistics 321, Engineering 319 or Digital Engineering 319 or are concurrently enrolled in Statistics 321 or Engineering 319.

Parametric and simulation-based hypothesis testing, and associated errors. Confidence intervals and hypothesis testing for differences between two parameters, both parametric and simulation-based. Tests of association and goodness-of-fit. Statistical modelling and parametric testing of both the simple and multiple-model. Diagnostic checking. Analysis of variance. Course Hours:3 units; (3-1) Prerequisite(s):Statistics 213. Antirequisite(s):Credit for Statistics 217 and either Statistics 205 or 327 will not be allowed. Not available to students who have previous credit for one of Statistics 321, Engineering 319 or Digital Engineering 319 or are concurrently enrolled in Statistics 321 or Engineering 319.

A calculus-based introduction to probability theory and applications. Elements of probabilistic modelling, Basic probability computation techniques, Discrete and continuous random variables and distributions, Functions of random variables, Expectation and variance, Multivariate random variables, Conditional distributions, Covariance, Conditional expectation, Central Limit Theorem, Applications to real-world modelling. Course Hours:3 units; (3-1T) Prerequisite(s):Mathematics 267 or 277. Antirequisite(s):Credit for Statistics 321 and Engineering 319 will not be allowed. Notes:Statistics 205, 213, 217, and 327 are not available to students who have previous credit for one of Statistics 321, Engineering 319 or Digital Engineering 319 or are concurrently enrolled in Statistics 321, Engineering 319 or Digital Engineering 319.

Statistics and their distributions. Introduction to statistical inference through point estimation and confidence interval estimation of a population parameter. Properties of statistics including unbiasedness and consistency in estimation. Single parameter hypothesis testing, Type I and Type II Error. Multi-parameter estimation through confidence interval estimation and hypothesis testing. The analysis of bivariate data through simple linear regression, including inferences on the parameters of the linear model and the analysis of variance. Chi-square test of independence and goodness of fit test. Course Hours:3 units; (3-1T) Prerequisite(s):Statistics 321. Antirequisite(s):Credit for Statistics 323 and Data Science 305 will not be allowed.

Statistics for the Physical and Environmental Sciences

Introduction to the collection of data. Probability and probability distributions. Single and Multi-sample estimation of distribution parameters. Regression and Goodness of Fit tests. Experimental Design and Analysis of Variance. Course Hours:3 units; (3-1) Prerequisite(s):3 units from Mathematics 249, 265 or 275. Antirequisite(s):Credit for Statistics 327 and any one of Statistics 205, 213 or 217 will not be allowed. Notes:Statistics 327 is not available to students who have previous credit for one of Statistics 321, Engineering 319 or Digital Engineering 319 or are concurrently enrolled in Statistics 321, Engineering 319 or Digital Engineering 319.

Markov chains. Limit distributions for ergodic and absorbing chains. Classification of states, irreducibility. The Poisson process and its generalizations. Continuous-time Markov chains. Brownian motion and stationary processes. Renewal theory. Course Hours:3 units; (3-0) Prerequisite(s):Statistics 321. Antirequisite(s):Credit for Statistics 407 and either 507 or Mathematics 585 will not be allowed.

An advanced examination of core concepts in mathematical statistics, including the multivariate normal distribution, limit distributions, sufficient statistics, completeness of families of distributions, exponential families, likelihood ratio tests, chi-square tests, and the analysis of variance. Additional topics and examples relating to sequential tests, non-parametric methods, Bayesian statistical modelling, and the general linear model may also be explored. Course Hours:3 units; (3-0) Prerequisite(s):Statistics 323.

Introduction to questionnaire design of sample surveys. Treatment of the various sampling methodologies used in population parameter estimation. Ratio and regression estimation. Sampling weights and variance estimation of statistics. Estimation of population size and density. Non-response. Course Hours:3 units; (3-0) Prerequisite(s):3 units from Statistics 217, 323, 327, Data Science 305, Engineering 319, Digital Engineering 319, Psychology 300, 301, 312, or Sociology 311.

Introduction to the design of experiments and the statistical analysis of data. Analysis of variance in the response variable and adequacy of the model. Multiple comparison methods. Extensions to completely randomized block, latin-squares, and factorial experimental design. Introduction to nested and split-plot design, with emphasis on statistical software usage. Course Hours:3 units; (3-0) Prerequisite(s):3 units from Statistics 217, 323, 327, Data Science 305, Engineering 319, Digital Engineering 319, Psychology 300, 301, 312, or Sociology 311.

Multiple linear regression model, parameter estimation, simultaneous confidence intervals and general linear hypothesis testing. Residual analysis and outliers. Model selection: best regression, stepwise regression algorithms. Transformation of variables and non-linear regression. Applications to forecasting. Variable selection in high-dimensional data using linear regression. Computer analysis of practical real world data. Course Hours:3 units; (3-1T) Prerequisite(s):Statistics 323 or Data Science 305; and Mathematics 211 or 213.

Fundamental topics in biostatistics, including descriptive statistics, graphical presentation of data, analysis of variance (ANOVA), study designs, contingency tables, measures of association, tests of significance, categorical data analysis, regression, time to event data analysis. Course Hours:3 units; (3-0) Prerequisite(s):Statistics 323 or Data Science 305.

An introduction to the theory and tools to conduct time series analysis, with the emphasis on modelling and forecasting using a software. Stationarity, white noise, autocorrelation, partial autocorrelation, and linear predictor. Stationary ARIMA models, seasonality and trends. Model fitting, diagnostics and forecasting. Additional topics may include state space models, spectral analysis of time series, and GARCH models. Course Hours:3 units; (3-1T) Prerequisite(s):Statistics 429.

A capstone course intended for students in their final year of study. The emphasis is on how to address real world scientific and social issues by applying the various statistical methods acquired in the earlier years in a unified and appropriate way. This involves method selection, data handling, statistical computing, consulting, report writing and oral presentation, team work, and ethics. Course Hours:3 units; (3-0) Prerequisite(s):6 units from Statistics 423, 425, 429 and 505.

Fundamentals of Bayesian inference, single and multiparameter models, hierarchical models, regression models, generalized linear models, advanced computational methods, Markov chain Monte Carlo. Course Hours:3 units; (3-0) Prerequisite(s):Statistics 323; and Mathematics 267 or 277. Antirequisite(s):Credit for Statistics 519 and 619 will not be allowed.

Study in advanced topics that may include reading projects, seminars, lectures, term papers and other aspects of training in theory or research methodology. Course Hours:3 units; (3-1) Prerequisite(s): Consent of the Department. MAY BE REPEATED FOR CREDIT

Introduction to statistical computing; random numbers generation; Monte Carlo methods (variance reduction technique; computation of definite integrals); Optimizations; Numerical integrations. Course Hours:3 units; (3-1) Prerequisite(s):Statistics 323; and Mathematics 267 or 277.

Nature and properties of survival models; methods of estimating tabular models from both complete and incomplete data samples including actuarial, moment and maximum likelihood techniques; estimations of life tables from general population data; Kaplan-Meier estimator and Nelson-Allan estimator; the accelerated failure time model; the Cox proportional hazards model; model building and high-dimensional survival data analysis. Course Hours:3 units; (3-1T) Prerequisite(s):Statistics 429. Antirequisite(s):Credit for Statistics 533 and either 633 or 433 will not be allowed.

Description and inference for binomial and multinomial observations using proportions and odds ratios; multi-way contingency tables; generalized linear models for discrete data; logistic regression for binary responses; multi-category logit models for nominal and ordinal responses; loglinear models, and inference for matched-pairs and correlated clustered data. Course Hours:3 units; (3-1T) Prerequisite(s):Statistics 429.

Introduction and linear regression; classification; regularization; model assessment and selection; support vector machines; unsupervised learning; tree-based methods; additional topics selected by course instructor. Course Hours:3 units; (3-0) Prerequisite(s):Statistics 429. Antirequisite(s):Credit for Statistics 543 and 641 will not be allowed.

A professional skills course, focusing on the development of technical proficiencies that are essential for students to succeed in their future careers as practicing statistician in academia, government, or industry. The emphasis is on delivering professional presentations and using modern statistical research tools. A high level of active student participation is required. Course Hours:1.5 units; (3S-0) Prerequisite(s):Admission to a graduate program in Mathematics and Statistics or consent of the Department. Also known as:(formerly Statistics 621) MAY BE REPEATED FOR CREDIT NOT INCLUDED IN GPA

The content of this course is decided from year-to-year in accordance with graduate student interest and instructor availability. Topics include but are not restricted to: Advanced Design of Experiments, Weak and Strong Approximation Theory, Asymptotic Statistical Methods, the Bootstrap and its Applications, Generalized Additive Models, Order Statistics and their Applications, Robust Statistics, Statistics for Spatial Data, Statistical Process Control, Time Series Models. Course Hours:3 units; (3-0) Prerequisite(s):Admission to a graduate program in Mathematics and Statistics or consent of the Department. MAY BE REPEATED FOR CREDIT

Descriptive statistics; probability theory; statistical estimation/inference; power analysis; regression analysis; anova; logistic regression analysis; non-parametric tests; factor analysis; discriminant analysis; Cox's Proportional Hazard Model. Course Hours:3 units; (3-1) Prerequisite(s):Admission to a graduate program in Mathematics and Statistics or consent of the Department. Also known as:(formerly Statistics 601.14)

Fundamentals of Bayesian inference, single and multiparameter models, hierarchical models, regression models, generalized linear models, advanced computational methods, Markov chain Monte Carlo. Course Hours:3 units; (3-0) Prerequisite(s):Admission to a graduate program in Mathematics and Statistics or consent of the Department. Antirequisite(s):Credit for Statistics 619 and 519 will not be allowed.

Normal distribution. Statistical inference: confidence regions, hypothesis tests, analysis of variance, simultaneous confidence intervals. Principal components. Factor Analysis. Discrimination and classification. Canonical correlation analysis. Course Hours:3 units; (3-0) Prerequisite(s):Admission to a graduate program in Mathematics and Statistics or consent of the Department. Antirequisite(s):Credit for Statistics 625 and 525 will not be allowed.

Unconstrained optimization methods, simulation and random number generation, Bayesian inference and Monte Carlo methods, Markov chain Monte Carlo, non-parametric inference, classical inference and other topics. An emphasis will be placed on computational implementation of algorithms. Course Hours:3 units; (3-0) Prerequisite(s):Admission to a graduate program in Mathematics and Statistics or consent of the Department.

Advanced topics in survival models such as the product limit estimator, the cox proportional hazards model, time-dependent covariates, types of censorship. Course Hours:3 units; (3-0) Prerequisite(s):Admission to a graduate program in Mathematics and Statistics or consent of the Department. Antirequisite(s):Credit for Statistics 633 and 533 will not be allowed.

Exponential family of distributions, binary data models, loglinear models, overdispersion, quasi-likelihood methods, generalized additive models, longitudinal data and generalized estimating equations, model adequacy checks. Course Hours:3 units; (3-0) Prerequisite(s):Admission to a graduate program in Mathematics and Statistics or consent of the Department.

Topics include but are not restricted to selections from: linear approximations; model specification; various iterative techniques; assessing fit; multiresponse parameter estimation; models defined by systems of differential equations; graphical summaries of inference regions; curvature measures. Course Hours:3 units; (3-0) Prerequisite(s):Admission to a graduate program in Mathematics and Statistics or consent of the Department.

Introduction and Linear Regression; Classification; Regularization; Model Assessment and Selection; Support Vector Machines; Unsupervised Learning; Tree-Based Methods; Other Topics (e.g., Neural Networks, Graphical Models, High-Dimensional Data). Course Hours:3 units; (3-0) Prerequisite(s):Admission to a graduate program in Mathematics and Statistics or consent of the Department. Antirequisite(s):Credit for Statistics 641 and 543 will not be allowed.

Probability spaces, integration, expected value, laws of large numbers, weak convergence, characteristic functions, central limit theorems, limit theorems in Rd, conditional expectation, introduction to martingales. Course Hours:3 units; (3-0) Prerequisite(s):Admission to a graduate program in Mathematics and Statistics or consent of the Department.

Stopping times, renewal theory, martingales, almost sure convergence, Radon-Nikodym derivatives, Doob’s inequality, square integrable martingales, uniform integrability, Markov chains, stationary measure, Birkhoff’s Ergodic Theorem, Brownian motion, stopping times, hitting times, Donsker’s Theorem, Brownian bridge, laws of the iterated logarithm. Course Hours:3 units; (3-0) Prerequisite(s):Statistics 701 and admission to a graduate program in Mathematics and Statistics or consent of the Department.

Statistical models, likelihoods, maximum likelihood estimators, likelihood ratio, Wald and score tests, confidence intervals, bounds and regions, Bayesian estimation and testing, basic large sample theory, estimating equations, jackknife, bootstrap and permutation. Course Hours:3 units; (3-0) Prerequisite(s):Admission to a graduate program in Mathematics and Statistics or consent of the Department.

Likelihood ratio (LR), union-intersection, most powerful, unbiased and invariant tests, Neyman-Pearson Lemma, Karlin-Rubin Theorem, confidence interval (CI), pivotal quantities, shortest length and shortest expected length CI, uniformly most accurate CI, confidence region, simultaneous CI, large-sample tests (Wald’s, score, LR tests), Bayesian hypothesis testing, analysis of variance and linear models. Course Hours:3 units; (3-0) Prerequisite(s):Statistics 721 and admission to a graduate program in Mathematics and Statistics or consent of the Department.