## Statistics STAT

Instruction offered by members of the Department of Mathematics and Statistics in the Faculty of Science.

Department Head - T. Bisztriczky

Note: Not every 400- and 500-numbered Statistics course is offered every year. Check with the divisional office to plan for the upcoming cycle of offered courses.

Note: For listings of related courses, see Actuarial Science Applied Mathematics, Mathematics, and Pure Mathematics.

Note: Credit towards degree requirements will be given for only one of Anthropology 307, Applied Psychology 301/303, Engineering 319, Political Science 399, Psychology 312, Sociology 311, Statistics 201/211, 213/217, 327, 333, 357; that one being a course(s) appropriate to the degree program.

Note: Statistics 201, 211, 213, 217, 327, 333, 357 are not available to students who have previous credit for Mathematics 321 or are concurrently enrolled in Mathematics 321.

## Junior Courses

Students requiring one half course in Statistics should take Statistics 211.

### Statistics 201 H(3-1T)

#### Elements of Finite Probability

Sets and events, counting techniques. Axioms of probability, conditioning and independence, Bayes' theorem. Random variables and their distributions. Expectations, variances and the law of large numbers.

**
Prerequisites:
** Pure Mathematics 30 or Mathematics II (offered by Continuing Education).

**
Note:
** See the statements regarding credit which appear at the beginning of the Statistics course listings.

### Statistics 211 H(3-1T)

#### Concepts of Statistics

The systematic treatment of fundamental statistical ideas culminating in the discussion of parameter estimation and hypotheses testing.

**
Prerequisites:
** Pure Mathematics 30 or Mathematics II (offered by Continuing Education).

**
Note:
** See the statements regarding credit which appear at the beginning of the Statistics course listings.

### Statistics 213 H(3-2)

#### Introduction to Statistics I

Collection and presentation of data, introduction to probability, including Bayes' law, expectations and distributions. Properties of the normal curve. Introduction to estimation and hypothesis testing.

**
Prerequisites:
** Pure Mathematics 30 or Mathematics II (offered by Continuing Education).

**
Note:
** See the statements regarding credit which appear at the beginning of the Statistics course listings.

### Statistics 217 H(3-2)

#### Introduction to Statistics II

Estimation of population parameters; confidence intervals for means; choice of sample size. Tests of hypotheses including 2-sample tests and paired comparisons. The Chi-squared tests for association and goodness-of-fit. Regression and correlation; variance estimates; tests for regression and correlation coefficients. Non-parametric methods and associated tests. Time series, forecasting.

**
Prerequisites:
** Statistics 213 or consent of the Division.

**
Note:
** See the statements regarding credit which appear at the beginning of the Statistics course listings.

## Senior Courses

### Statistics 327 H(3-1)

#### Environmental Statistics

Sampling environmental populations. Probability distributions. Estimating distribution parameters and quantiles. Hypothesis tests. Goodness of fit tests. Detecting trends. Outlier detection. Censored data.

**
Prerequisites:
** Mathematics 249 or 251 or Applied Mathematics 217.

**
Note:
** See the statements regarding credit which appear at the beginning of the Statistics course listings.

### Statistics 333 H(3-3)

#### Statistics for the Life Sciences

Exploratory data analysis, relationships between variables, elementary probability, random variables, statistical inference, application of statistical methods to medical and biological problems.

**
Prerequisites:
** Pure Mathematics 30 or Mathematics II (offered by Continuing Education).

**
Note:
** See the statements regarding credit which appear at the beginning of the Statistics course listings.

### Statistics 357 H(3-1T)

#### Statistics for the Physical Sciences

Exploratory data analysis. Fundamentals of probability. Discrete and Continuous distributions. Introduction to statistical reasoning. Interval estimation. Hypothesis testing. Simple and multiple linear regression. Experimental design. Analysis of variance. Factorial design.

**
Prerequisites:
** Mathematics 251 or 249 or Applied Mathematics 217.

**
Note:
** See the statements regarding credit which appear at the beginning of the Statistics course listings.

### Statistics 407 H(3-1T)

#### Applied Probability

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. Introduction to basic simulation methods.

**
Prerequisites:
** Mathematics 321.

### Statistics 409 H(3-0)

#### Theoretical Probability

Elementary measure theory, zero-one laws, weak and strong laws of large numbers, characteristic functions, central limit theorems and infinitely divisible distributions.

**
Prerequisites:
** Mathematics 323.

### Statistics 419 H(3-0)

(Pure Mathematics 419)

#### Information Theory and Error Control Codes

Information sources, entropy, channel capacity, development of Shannon's theorems, development of a variety of codes including error correcting and detecting codes.

**
Prerequisites:
** Mathematics 311 and 321 or any Statistics course, or consent of the Division.

**
Note:
** Credit for both Statistics 419 (Pure Mathematics 419) and Statistics 405 will not be allowed.

### Statistics 421 H(3-1T)

#### Mathematical Statistics

Multivariate Normal distribution. Limit distributions. Sufficient statistics. Completeness of families of distributions. Exponential families. Likelihood ratio tests. Chi-square tests. Analysis of variance. Sequential tests. Introduction to nonparametric methods, Bayesian theory, the general linear model.

**
Prerequisites:
** Mathematics 323.

### Statistics 423 H(3-1T)

#### Sampling Theory of Surveys

Principles of sampling. Questionnaire design. Various types of sampling designs: simple random, stratified, systematic, cluster, multi-stage cluster. Ratio and regression estimates. Estimation of required sample size. Estimation of population size and density. Problems of nonresponse.

**
Prerequisites:
** Any one of Statistics 217, 327, 333, 357, Applied Psychology 301, Engineering 319, Mathematics 323, Psychology 312, Sociology 311 or consent of the Division.

### Statistics 425 H(3-1T)

#### Experimental Design

The objective and structure of an experiment, cause and effect, randomization, the estimation of error, replication, interaction, confounding. Using a computer as an aid in the analysis.

**
Prerequisites:
** Any one of Statistics 217, 327, 333, 357, Applied Psychology 301, Engineering 319, Mathematics 323, Psychology 312, Sociology 311 or consent of the Division.

### Statistics 429 H(3-1T)

#### Applied Regression Analysis

Multiple linear regression model including parameter estimation, simultaneous confidence intervals and general linear hypothesis testing using matrix algebra. Applications to forecasting. Residual analysis and outliers. Model selection: best regression, stepwise regression algorithms. Transformation of variables and non-linear regression. Computer analysis of practical real world data.

**
Prerequisites:
** Mathematics 323.

**
Note:
** Credit for both Statistics 429 and 431 will not be allowed.

**
Note:
** Statistics 421 is highly recommended as preparation.

### Statistics 433 H(3-1T)

#### Survival Models

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.

### Statistics 437 H(3-1T)

#### Risk Theory

Economics of insurance; individual risk models for short term; collective risk models for single period; collective risk models over an extended period; application of risk theory to insurance.

**
Prerequisites:
** Mathematics 323.

### Statistics 505 H(3-1T)

#### Time Series Analysis

Trend fitting, auto-regressive schemes, moving average models, periodograms, second-order stationary processes, ARCH models, statistical software for time series. Additional topics may include Bayesian analysis, spectral theory, Kalman filtering.

**
Prerequisites:
** Statistics 429 or consent of the Division.

### Statistics 509 H(3-0)

#### Operations Research

Topics selected from: decision analysis, linear programming, dynamic programming, integer programming, probabilistic models of queues and inventories, project scheduling, systems reliability.

**
Prerequisites:
** Mathematics 323 or consent of the Division.

**
Note:
** Credit for both Statistics 509 and Actuarial Science 435 will not be allowed.

### Statistics 517 H(3-1)

#### Practice of Statistics

Intended for students in their final year of study. Introduction to real-world statistical practice. Model selection. Messy data. Statistical software. Report writing and presentation. Working in groups. Ethical considerations in statistics.

**
Corequisites:
** Prerequisite or Corequisite: Statistics 429.

**
Note:
** Not open to students with Statistics 511, 513 or 515.

### Statistics 519 H(3-0)

#### Bayesian Statistics

Fundamentals of Bayesian inference, single and multiparameter models, hierarchical models, regression models, generalized linear models, advanced computational methods, Markov chain Monte Carlo.

**
Prerequisites:
** Mathematics 323 or consent of the Division.

**
Note:
** Statistics 421 is recommended.

### Statistics 523 H(3-0)

#### Nonparametric Statistics

Nonparametric estimation and tests of hypotheses. Distributions useful to handle nonparametric inference. Distribution-free tests. Asymptotic Theory.

**
Corequisites:
** Prerequisite or Corequisite: Mathematics 323 or consent of the Division.

**
Note:
** May not be offered every year. Consult the department for listings.

### Statistics 525 H(3-1)

#### Multivariate Analysis

Normal distribution. Statistical inference: confidence regions, hypothesis tests, analysis of variance, simultaneous confidence intervals. Principal components. Factor Analysis. Discrimination and classification. Canonical correlation analysis.

**
Prerequisites:
** Statistics 421 or consent of the Division.

**
Note:
** May not be offered every year. Consult the department for listings.

### Statistics 529 H(3-1)

#### Special Topics in Applied Statistics

Content of the course will vary from year to year. Consult the Statistics Division for information on choice of topics.

**
Prerequisites:
** Consent of the Division.

**
MAY BE REPEATED FOR CREDIT
**

### Statistics 531 H(3-1)

#### Monte Carlo Methods and Statistical Computing

Introduction to a variety of statistical languages and packages and introductory statistical programming in SPLUS. Pseudo-random variate generation. Bootstrapping. Variance reduction techniques. Computation of definite integrals. Model design and simulation, with applications.

**
Prerequisites:
** Mathematics 323 or consent of the Division.

**
Note:
** Statistics 421 is highly recommended as preparation.

## Graduate Courses

Note: Some 500- and 600-level statistics courses may have concurrent lectures. Extra work in these courses (e.g., extra assignments, advanced examination questions, a term project) will be required for credit at the 600 level.

### Statistics 601 H(3-0)

#### Topics in Probability and Statistics

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.

**
MAY BE REPEATED FOR CREDIT
**

### Statistics 603 H(3-1)

(formerly Statistics 601.14)

#### Applied Statistics for Nursing Research

Descriptive statistics; probability theory; statistical estimation/inference; power analysis; regression analysis; anova; logistic regression analysis; nonparametric tests; factor analysis; discriminant analysis; Cox's Proportional Hazard Model.

### Statistics 619 H(3-0)

#### Bayesian Statistics

Fundamentals of Bayesian inference, single and multiparameter models, hierarchical models, regression models, generalized linear models, advanced computational methods, Markov chain Monte Carlo.

**
Note:
** Lectures may run concurrently with Statistics 519.

### Statistics 621 Q(2S-0)

#### Research Seminar

Reports on studies of the literature or of current research.

**
Note:
** All graduate students in Mathematics and Statistics are required to participate in one of Applied Mathematics 621, Pure Mathematics 621, Statistics 621 each semester.

**
MAY BE REPEATED FOR CREDIT
**

**
NOT INCLUDED IN GPA
**

### Statistics 625 H(3-0)

#### Multivariate Analysis

Normal distribution. Statistical inference: confidence regions, hypothesis tests, analysis of variance, simultaneous confidence intervals. Principal components. Factor Analysis. Discrimination and classification. Canonical correlation analysis.

**
Note:
** Lectures may run concurrently with Statistics 525.

### Statistics 633 H(3-0)

#### Survival Models

Advanced topics in survival models such as the product limit estimator, the cox proportional hazards model, time-dependent covariates, types of censorship.

### Statistics 635 H(3-0)

#### Generalized Linear Models

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.

### Statistics 637 H(3-0)

#### Nonlinear Regression

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 DEs; graphical summaries of inference regions; curvature measures.

### Statistics 639 H(3-0)

#### Conference Course in Actuarial Modelling

Topics in advanced actuarial theory and practice, such as: insurance risk models; practical analysis of extreme values; advanced property and casualty rate making; actuarial aspects of financial theory.

**
MAY BE REPEATED FOR CREDIT
**

In addition to the numbered and titled courses shown above, the department offers a selection of advanced level graduate courses specifically designed to meet the needs of individuals or small groups of students at the advanced doctoral level. These courses are numbered in the series 800.01 to 899.99. Such offerings are, of course, conditional upon the availability of staff resources.