Course Listings: Winter Term 2018-19

Introduction to data analysis with a focus on regression. Initial Examination of data. Correlation. Simple and multiple regression models using least squares. Inference for regression parameters, confidence and prediction intervals. Diagnostics and remedial measures. Interactions and dummy variables. Variable selection. Least squares estimation and inference for non-linear regression.

Prerequisite:

• STA238H1/STA248H1/STA255H1/STA261H1/ECO227Y1
• CSC108H1/CSC120H1/CSC121H1/CSC148H1
• STA1002H

Analysis of variance for one-and two-way layouts, logistic regression, loglinear models, longitudinal data, introduction to time series.

Prerequisite: STA1001H or equivalent

Design of surveys, sources of bias, randomized response surveys. Techniques of sampling; stratification, clustering, unequal probability selection. Sampling inference, estimates of population mean and variances, ratio estimation., observational data; correlation vs. causation, missing data, sources of bias.

Exclusion: STA322H1
Prerequisite: ECO220Y1/ECO227Y1/GGR270Y1 / PSY202H1/SOC300Y1/STA221H1/STA255H1/261H1/248H1

This cross-listed course covers a number of topics used in the design and analysis of experiments. The course is intended for students of statistics as well as students of other disciplines (eg. engineering, experimental science, etc.) who will use experimental design and analysis in their work.

The course will cover the following topics: randomization, blocking Latin squares, balanced incomplete block designs, factorial experiments, confounding and fractional replication, components of variance, orthogonal polynomials, response surface methods. Additional topics will be covered based on students’ interest as time permits.

Prerequisite: STA302H/352Y/ECO327Y/ECO357Y or permission of instructor.

Practical techniques for the analysis of multivariate data; fundamental methods of data reduction with an introduction to underlying distribution theory; basic estimation and hypothesis testing for multivariate means and variances; regression coefficients; principal components and the partial multiple and canonical cor relations; multivariate analysis of variance;  classification and the linear discriminant function. The use of R software should be  expected.

Prerequisite: STA302H/352Y Recommended Preparation: MAT223H/240H

Discrete and continuous time processes with an emphasis on Markov, Gaussian and renewal processes. Martingales and further limit theorems. A variety of applications taken from some of the following areas are discussed in the context of stochastic modeling: Information Theory, Quantum Mechanics, Statistical Analyses of Stochastic Processes, Population Growth Models, Reliability, Queuing Models, Stochastic Calculus, Simulation (Monte Carlo Methods).

Prerequisite: STA347H or equivalent knowledge of probability theory; and MAT235Y/237Y or equivalent knowledge of multivariate calculus and basic real analysis.

Data acquisition trends in the environmental, physical and health sciences are increasingly spatial in character and novel in the sense that modern sophisticated methods are required for analysis.

This course will cover different types of random spatial processes and how to incorporate them into mixed effects models for Normal and non-Normal data.

Students will be trained in a variety of advanced techniques for analyzing complex spatial data and, upon completion, will be able to undertake a variety of analyses on spatially dependent data, understand which methods are appropriate for various research questions, and interpret and convey results in the light of the original questions posed. 

Statistical genetics is an important data science research area with direct impact on population health, and this course provides an INTRODUCTION to its concepts and fundamentals.

We start with an overview of genetic studies to have a general understanding of its goal and study design.

We then introduce the basic genetic terminologies necessary for the ensuing discussion of the various statistical methods used for analyzing genetic data. The specific topics include population genetics, principles of inheritance, likelihood for pedigree data, aggregation, heritability and segregation analyses, map and linkage analysis, population-based and family-based association studies and genome-wide association studies.

The flow of the content generally follows that of the The Fundamentals of Modern Statistical Genetics by Laird and Lange, and additional materials will be provided.

Participating students do not need formal training in genetics, but they are expected to have statistical knowledge at the level of STA303 – Methods of Data Analysis or equivalent.

This course will consider topics in statistics that have played a role in the development of techniques for data mining and machine learning. We will cover linear methods for regression and classification, nonparametric regression and classification methods, generalized additive models, aspects of model inference and model selection, model averaging and tree bassed methods.

Prerequisite: Either STA302H or CSC411H

The course will focus on generalized linear models (GLM) and related methods, such as generalized additive model involving nonparametric regression, generalized estimating equations (GEE) and generalized linear mixed models (GLMM) for longitudinal data. This course is designed for Master and PhD students in Statistics, and is REQUIRED for the Applied paper of the PhD Comprehensive Exams in Statistics.

We deal with a class of statistical models that generalizes classical linear models to include many other models that have been found useful in statistical analysis, especially in biomedical applications. The course is a mixture of theory and applications and includes computer projects featuring R (S+) or/and SAS programming.

Topics: Brief review of likelihood theory, fundamental theory of generalized linear models, iterated weighted least squares, binary data and logistic regression, epidemiological study designs, counts data and log-linear models, models with constant coefficient of variation, quasi-likelihood, generalized additive models involving nonparametric smoothing, generalized estimating equations (GEE) and generalized linear mixed models (GLMM) for longitudinal data.

Prerequisite: Advanced Calculus, Linear Algebra, STA 347 and STA 422 (upper-division courses on probability and statistical inference) or equivalent, STA 302 (linear regression), Statistical Computing using R (S+) or/and SAS (alternative softwares are allowed). However, please be advised that I may not be familiar with the software of your choice resulting in limited assistance.

An overview of methods and problems in the analysis of time series data. Topics include: descriptive methods, filtering and adjustment, spectral estimation, bivariate time series models.

The course will cover the following topics:

• Theory of stationary processes, linear processes
• Elements of inference in time domain with applications
• Spectral representation of stationary processes
• Elements of inference in frequency domain with applications
• Theory of prediction (forecasting) with applications to ARMA processes, inference and forecasting
• Non-stationarity and seasonality, ARIMA and SARIMA processes

Further topics, time permitting: multivariate models; GARCH models; state-space models.

STA 2211H is a follow-up course to STA 2111F, designed for Master’s and Ph.D. level students in statistics, mathematics, and other departments, who are interested in a rigorous, mathematical treatment of probability theory using measure theory.

Specific topics to be covered include:

• weak convergence,
• characteristic functions,
• central limit theorems,
• the Radon-Nykodym Theorem,
• Lebesgue Decomposition,
• conditional probability and expectation,
• martingales
• Kolmogorov’s Existence Theorem.

This course is designed for graduate students in Statistics and Biostatistics.

A continuation of STA2112. Topics include: Bayesian methods, minimum variance estimation, asymptotic efficiency of maximum likelihood estimation, interval estimation and hypothesis testing, linear and generalized linear models, goodness-of-fit for discrete and continuous data.

Prerequisite: STA2112

Overview

This course is designed to provide graduate students with experience in statistical consulting. Students are active participants in research projects brought to the Statistical Consulting Service (SCS) of the Department of Statistics.

The course is offered over the two sessions, fall (September-December) and winter (January-April). The overall workload is approximately equivalent to a half graduate course and students receive a half credit.

Students are not expected to have had any experience as consultants. The purpose of the course is to provide this experience so that graduates will be better able to function in such an environment when they have completed the course. The course also provides students with the opportunity to become familiar with statistical software packages such as The SAS System. There is supervision and assistance to novice consultants.

Content

There is some classroom instruction at the start of the term, and meetings occasionally are called to discuss special topics and for students to compare experiences. Students serve as apprentice statisticians and work under the guidance of the instructor and the SCS Coordinator on individual projects. Projects are assigned to students as they come in to the SCS. There are periods of inactivity when there are no projects and other times are very busy. The pattern of work is more like that associated with a business or working environment than a traditional course. While some consideration is taken of other academic demands on students, those enrolling must be aware that work on projects may require precedence at times.

Evaluation

Students will be graded on the quality of their work as stati stical consultants. This involves the ability to do work in a timely fashion, the quality of advice provided and the quality of the presentation of advice and written work to clients.

Prerequisite: Students should have taken some applied statistics courses such as an undergraduate regression course. Also undergraduate courses in applied statistics, sample survey, design of experiments and time series analysis are recommended but these are not required. Also taking some of the other 2000 level applied statistics courses is recommended as this course will serve as an excellent opportunity to put the content of these courses to work.

Limited fluctuation or American credibility, on a full and partial basis. Greatest accuracy or European credibility, predictive distributions and the Bayesian premium, credibility premiums including the Buhlmann and Buhlmann-Straub models, empirical Bayes nonparametric and semi-parametric parameter estimation. Simulation, random numbers, discrete and continuous random variable generation, discrete event simulation, statistical analysis of simulated data and validation techniques.

Prerequisite: Consult the instructor concerning necessary background for this course

In this course we will study techniques and algorithms for creating effective data visualizations based on principles from graphic design, visual art, perceptual psychology, and cognitive science. This course is targeted both towards students interested in using visualization in their own work, as well as students interested in building better visualization tools and systems.

Please note that this course can only be taken by PhD students in the Department of Statistical Sciences.

This is the Department’s core graduate course in statistical theory. It covers the basic principles of statistical inference, their application to a variety of statistical models, and some generalizations to more complex settings.

Prerequisite: STA2112H and STA2212H or equivalent. (STA2111H and STA2211H may be co-requisites). Some familiarity with measure theory is very useful. The text includes some supplementary material on this.

This course focuses on advanced theory and modeling of financial derivatives. The topics include, but are not limited to: HJM interest rate models, LFM and LSM market models; foreign exchange options; defaultable bonds; credit default swaps, equity default swaps and collateralized debt obligations; intensity and structural based models; jump processes and stochastic volatility; commodity models. As well, students are required to complete a project, write a report and present a topic of current research interest.
 

Prerequisite: STA 2503 or equivalent knowledge.

Overview

New inference methods allow us to train learn generative latent-variable models. These models can generate novel images and text, find meaningful latent representations of data, take advantage of large unlabeled datasets, and even let us do analogical reasoning automatically. However, most generative models such as GANs and variational autoencoders currently have pre-specified model structure, and represent data using fixed-dimensional continuous vectors.

This seminar course will develop extensions to these approaches to learn model structure, and represent data using mixed discrete and continuous data structures such as lists of vectors, graphs, or even programs. The class will have a major project component, and will be run in a similar manner to Differentiable Inference and Generative Models.

Prerequisite: This course is designed to bring students to the current state of the art, so that ideally, their course projects can make a novel contribution. A previous course in machine learning such as CSC321, CSC411, CSC412, STA414, or ECE521 is strongly recommended. However, the only hard requirements are linear algebra, basic multivariate calculus, basics of working with probability, and basic programming skills.

The course will cover modeling, estimation and inference of non-stationary time series. In particular, we will deal with statistical inference of trends, quantile curves, time-varying spectra and functional linear models related to non-stationary time series. With the recent advances in various fields, a systematic account of non-stationary time series analysis is needed.

The concept of statistical evidence is central to the field of statistics. In spite of many references to “the evidence” in statistical applications, it is fair to say that there is no definition of this that achieves broad support in the sense of serving as the core of a theory of statistics. 

This course will examine the various attempts made to measure evidence in the statistical literature and why these are not entirely satisfactory. A proposal to base the theory of statistical inference on a particular measure, the relative belief ratio, is discussed and how this fits into a general theory of statistical reasoning.

This course provides an overview of the core areas of demography (fertility, mortality and migration) and the techniques to model such processes.

The course will cover life table analysis, measures of fertility and nuptiality, mortality and migration models, and statistical methods commonly used in demography, such as Poisson regression, survival analysis, and Bayesian hierarchical models.

The goal of the course is to equip students with a range of demographic techniques to use in their own research.