STAT Course Descriptions

Statistics (2009-2010)

Elementary probability, populations, samples and distributions with biological examples. Methods for data summary and presentation. Estimation, hypothesis testing, two-sample techniques and paired comparisons, regression, correlation. [Offered: F,W]

Empirical problem solving in software engineering. Measures of software reliability, maintainability and performance. Variation in software performance. Modelling structure and variation. Confidence intervals and hypothesis tests. Comparative studies and regression models. [Offered: F]

Descriptive statistics, probability, discrete and continuous random variables. Sampling distributions and simple hypothesis testing. Introduction to survey sampling. [Offered: F]

The laws of probability, discrete and continuous random variables, expectation, central limit theorem. [Offered: F,W]

Empirical problem solving, measurement systems, causal relationships, statistical models, estimation, confidence intervals, tests of significance. [Offered: F, W]

The laws of probability, discrete and continuous random variables, expectation, central limit theorem.

Empirical problem solving, measurement systems, causal relationships, statistical models, estimation, confidence intervals, tests of significance.

STAT 240 is an advanced-level enriched version of STAT 230.

STAT 241 is an advanced-level enriched version of STAT 231.

This is an applications oriented course which prepares the nonmathematical student to use the computer as a research tool. Topics include aids for statistical analysis and the preparation of documents such as reports and theses. The course provides sufficient background for application to other problems specific to the individual's field.

Modeling the relationship between a response variable and several explanatory variables via regression models. Model diagnostics and improvement. Using regression models for forecasting, Exponential smoothing. Simple time series modeling. [Offered: W]

Planning sample surveys; simple random sampling; stratified sampling. Observational and experimental studies. Blocking, randomization, factorial designs. Analysis of variance. Applications of design principles. [Offered: F]

Statistical reporting using a software package for statistical calculations; numerical and graphical summaries, contingency tables, significance tests and confidence intervals; regression methods; analysis of data from comparative studies. [Offered: W]

Maximum likelihood estimation. Random variables and distribution theory. Generating functions. Functions of random variables. Limiting distributions. Large sample theory of likelihood methods. Likelihood ratio tests.

Modeling the relationship between a response variable and several explanatory variables (an output-input system) via regression models. Least squares algorithm for estimation of parameters. Hypothesis testing and prediction. Model diagnostics and improvement. Algorithms for variable selection. Nonlinear regression and other methods. [Offered: F,W,S]

Designing sample surveys. Probability sampling designs. Estimation with elementary designs. Observational and experimental studies. Blocking, randomization, factorial designs. Analysis of variance. Designing for comparison of groups. [Offered: F,S]

Review of basic probability. Generating functions. Theory of recurrent events. Markov chains, Markov processes, and their applications. [Offered: F,W,S]

Random variables and distribution theory, conditional expectations, moment and probability generating functions, change of variables, random walks, Markov chains, Markov processes. [Offered F,S]

Building and validation of stochastic simulation models useful in computing, operations research, engineering and science. Related design and estimation problems. Variance reduction. The implementation and analysis of simulation results. [Offered: W,S]

Approximation and optimization of noisy functions. Simulation from univariate and multivariate distributions, multivariate normal distribution, mixture distributions and introduction to Markov Monte Carlo. Introduction to supervised statistical learning including discrimination methods. [Offered: F,S]

Applications of regression models to business problems; model building, fitting and assessment. Applications of sample surveys to business; design and analysis of surveys; management of sample and non-sample error. [Offered: F,S]

Analysis of time series data in business; adjustment and over-adjustment; forecasting using simple models. Process thinking and improvement; design and analysis of process investigations. [Offered: F,W]

Application of regression and time series models in finance; multiple regression; algebraic and geometric representation of least squares; inference methods - confidence intervals and hypothesis tests, ANOVA, prediction; model building and assessment; time series modeling; autoregressive AR(1) models - fitting, assessment and prediction; moving average smoothing, seasonal adjustment; non-stationarity and differencing. [Offered: F]

Review of experimental designs in a regression setting; analysis of variance; replication, balance, blocking, randomization, and interaction; one-way layout, two-way layout, and Latin square as special cases; factorial structure of treatments; covariates; treatment contrasts; two-level fractional factorial designs; fixed versus random effects; split-plot and repeated-measures designs; other topics. [Offered: F,S]

Review of the normal linear model and maximum likelihood estimation; regression models for binomial, Poisson and multinomial data; generalized linear models; and other topics in regression modelling. [Offered: F]

Point processes. Renewal theory. Stationary processes. Selected topics. [Offered: F]

Statistical methods for improving processes based on observational data. Assessment of measurement systems. Strategies for variation reduction. Process monitoring, control and adjustment. Clue generation techniques for determining the sources of variability. Variation transmission. [Offered: W]

Introduction to and application of computational methods in statistical inference. Monte Carlo evaluation of statistical procedures, exploration of the likelihood function through graphical and optimization techniques including EM. Bootstrapping, Markov Chain Monte Carlo, and other computationally intensive methods. [Offered: W]

Given known group membership, methods which learn from data how to classify objects into the groups are treated. Review of likelihood and posterior based discrimination. Main topics include logistic regression, neural networks, tree-based methods and nearest neighbour methods. Model assessment, training and tuning. [Offered: F]

Visualization of high dimensional data including interactive methods directed at exploration and assessment of structure and dependencies in data. Methods for finding groups in data including traditional and modern methods of cluster analysis. Dimension reduction methods including multi-dimensional scaling, nonlinear and other methods. [Offered: F]

Model building. Multiple regression and forecasting. Exponential smoothing. Box-Jenkins models. Smoothing of seasonal data. [Offered: F,W,S]

Methods for finding surfaces in high dimensions from incomplete or noisy functional information. Both data adaptive and methods based on fixed parametric structure will be treated. Model assessment, training and tuning. [Offered: W]

Mathematical techniques used to price and hedge derivative securities in modern finance. Modelling, analysis and computations for financial derivative products, including exotic options and swaps in all asset classes. Applications of derivatives in practice. [Offered: F,W]

Discussion of inference problems under the headings of hypothesis testing and point and interval estimation. Frequentist and Bayesian approaches to inference. Construction and evaluation of tests and estimators. Large sample theory of point estimation. [Offered: W]

Sources of survey error. Probability sampling designs, estimation and efficiency comparisons. Distribution theory and confidence intervals. Generalized regression estimation. Software for survey analysis. [Offered: W]