STAT 631Introduction to Statistacl Methods in Health Informatics0.50 units
Exploratory data analysis and data visualization. Confounding, censoring, selection bais, study designs and meta-analysis. Statistical modelling for continuous and binary data. Use of a statistics package, such as SAS, to analyze case studies will be imporant throughout. This is open only to students registered in the Masters of Health Informatics plan.
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.
STAT 831Generalized Linear Models and Applications0.50 units
Review of normal linear regression and maximum likelihood estimation. Computational methods, including Newton-Raphson and iteratively reweighted least squares. Binomial regression; the role of the link function. Goodness-of-fit, goodness-of-link, leverage. Poisson regression models. Generalized linear models. Other topics in regression modelling.
STAT 835Statistical Methods for Process Improvement0.50 units
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.
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.
STAT 841Statistical Learning - Classification0.50 units
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.
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.
STAT 844Statistical Learning - Function Estimation0.50 units
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.
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 erivatives in practice.
STAT 850Estimation and Hypothesis Testing0.50 units
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.
Sources of survey error. Probability sampling designs, estimation and efficiency comparisons. Distribution theory and confidence intervals. Generalized regression estimation. Software for survey analysis.
Review of conditioning on sigma-fields; martingale theory (discrete and continuous-time) and applications; counting processes; Brownian motion; stochastic differential and integral equations and applications; general theory of Markov processes (including martingale problems and semigroup theory), diffusions; weak convergence of stochastic processes on function spaces; functional versions of the central limit theorem and strong laws; convergence of empirical processes.
STAT 906Computer Intensive Methods for Stochastic Models in Finance0.50 units
Review of basic numerical methods. Simulation of random variables, stochastic processes and stochastic models in finance. Numerical solution of deterministic and stochastic differential equations. Valuation of complex financial instruments and derivative securities. Project and paper.
Principles of Inference: sufficiency, conditionality, and likelihood; examples and counter examples; conditional inference and ancillarity. Theory of Hypothesis Testing: Neyman-Pearson lemma; similar tests; invariant tests. Asymptotic Theory: maximum likelihood and related theory; large-sample properties of parametric significance tests. Interval Estimation: confidence intervals and significance intervals; location and scale models, conditional intervals. Introduction to Decision Theory: loss and risk functions, admissibility; minimax and Bayes rules; prior and posterior analysis. The course content of Stat 850 is a presumed prerequisite for Stat 908.
Multiple time series modeling including transfer function and intervention analysis. Various special topics in time series such as outliers, robustness, order determination methods, Kalman filtering, sampling and aggregation, seasonal adjustments.
This course deals with methods of analyzing data on the time to failure with particular emphasis on the use of regression models for such data. Both parameteric and semi-parametric regression models will be considered.
This course is designed to teach students the appropriate techniques for analyzing data that is collected over time. This data could arise from biomedical, population public health studies as well as finance and actuarial science applications. The course will teach how to recognize the added complexity of longitudinal data versus the univariate response data which is typically seen in introductory and generalized linear model courses. The course emphasizes the importance of the covariance structure for longitudinal responses. The students will study the difference between subject-specific and population-averaged models and how to recognize problems where one or the other approach might be more appropriate. They will be expected to use statistical software in applications in order to analyze longitudinal data.
STAT 937Introduction to Biostatistics and Epidemiology0.50 units
Design of medical studies including cohort designs, case-control studies and clinical trials. Measures of association in epidemiological studies. Analysis of data from cohort studies, clinical trials and case-control studies. Other topics such as multiplicity in clinical trials, group randomized designs, sequential and group sequential procedures as time permits. Use of a statistical package (e.g. SAS or S-Plus) to analyze medical data.
This course will cover some of the basic tools of a statistical consultant. Topics will include the use of statistical packages, problem-solving techniques, discussion of common statistical consulting problems, effective communication of statistical concepts and management of consulting sessions.
The focus of this course is on the statistical modelling, estimation and inference and forecasting of nonlinear financial time series, with a special emphasis on volatility and correlation of asset prices and returns. Topics to be covered normally include: review on distribution and dynamic behaviour of financial time series, univariate and multivariate GARCH processes, long-memory time-series processes, stochastic volatility models, modelling of extreme values, copulas, realized volatility and correlation modelling for ultra high frequency data and continuous time models.