Graduate Course Offerings

The Department of Statistics offers a wide range of courses in theoretical and applied topics in Statistics, Probability and Actuarial Science and Mathematical Finance. Students are advised that they should discuss their academic background with the instructor before or at the first meeting of the course. Consult the timetable for the meeting information for each course.

Note: 1000 level courses cannot be taken for credit by graduate students in the Department of Statistics.

Note: New 4500 level courses are 0.25FCEs and last 6 weeks

2017-2018 Graduate Winter Timetable

 


STA1001H – Methods of Data Analysis I (also offered as undergraduate course STA302H1)

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: STA248H1/261H1/ECO220Y1(70%)/ ECO227Y1/(STA257H1/(STA250H1, STA255H1)) or equivalent

STA1002H – Methods of Data Analysis II  (also offered as undergraduate course STA303H1)

Analysis of variance for one-and two-way layouts, logistic regression, loglinear models, longitudinal data, introduction to time series.
Prerequisite: STA1001H or equivalent

STA1003H – Sample Surveys Theory (also offered as undergraduate course STA304H1)

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

STA1004H – Elementary Experimental Design (also offered as undergraduate course STA305H1)

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.

STA1007H – Statistics for Life and Social Scientists (also offered as undergraduate course STA429H1)

Consult the instructor for further details.

Prerequisite: Consult the instructor concerning necessary background for this course

STA1008H -Applied Statistics

Vocabulary of data analysis, Tests of statistical significance, Principles of research design, Introduction to unix, Introduction to SAS, Elementary significance tests, Multiple regression, Factorial ANOVA, Permutation tests, Power and sample size, Random effects models, Multivariate analysis of variance, Analysis of within-cases designs (repeated measures). If time permits, Categorical data analysis.

Prerequisite: Any introductory statistics class, taught by any department.

STA2004H Design of Experiments

A second course in design of experiments. Topics include: experiments vs observational studies, randomization and model-based inference, randomized blocks, Latin squares, incomplete block designs, factorial and fractional factorial designs, cross-over designs, confounding and aliasing, response surface designs and Taguchi methods, optimal design, Bayesian design.

Prerequisite: STA332H or equivalent

STA2005H – Applied Multivariate Analysis (also offered as undergraduate course STA437H1)

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; profile analysis and curve fitting for repeated measurements; classification and the linear discriminant function. There will be extensive use of statistical computing packages.

Prerequisite: STA302H/352Y

Recommended Preparation: MAT223H/240H

STA2006H Applied Stochastic Processes (also offered as undergraduate course STA447H1)

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.

STA2047H Stochastic Calculus

Brownian motion, stochastic integrals, stochastic differential equations, diffusions, Cameron-Martin-Girsanov formula, diffusion approximations, applications. The course will be mathematically rigorous and self-contained.

Prerequisite: No explicit prerequisites, but to understand the material, it is necessary to have a good understanding at the advanced undergraduate level of at least one of the following: Probability, Real Analysis, Differential Equations, Mathematical Finance.

STA2080H Fundamentals of Statistical Genetics(.5 FCE)(also offered as undergraduate course STA480H1)

Statistical analysis of genetic data is an important emerging research area with direct impact on population health. This course provides an introduction to the concepts and fundamentals of statistical genetics, including current research directions. The course includes lectures and hands-on experience with R programming and state-of-the-art statistical genetics software packages.

STA2101H Methods of Applied Statistics I (also offered as undergraduate course STA442H1)

Advanced topics in statistics and data analysis with emphasis on applications. Diagnostics and residuals in linear models, introductions to generalized linear models, graphical methods, additional topics such as random effects models, split plot designs, analysis of censored data, introduced as needed in the context of case studies.

Prerequisite: ECO374H1/ECO375H1/STA302H1; STA305H1

STA2102H Computational Techniques in Statistics (also offered as undergraduate course STA410H1)

This course will study how statistical computations are done, and develop students’ abilities to write programs for statistical problems that are not handled by standard packages. Students will learn the capabilities of the R statistical computing environment, and learn to program new statistical methods in that environment. R will be introduced as part of the course; no prior knowledge of it is necessary.

Prerequisite: This course is designed for graduate and senior undergraduate students in statistics, actuarial science, computer science or other fields where statistical computation is important.

Students should have a basic background in statistical methods (eg. at the level of STA302), and some prior experience with programming (eg. at the level of CSC108).

STA2104H Statistical Methods for Machine Learning and Data Mining (also offered as undergraduate course STA414H1)

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

STA2105H Nonparametric methods of inference (also offered as undergraduate course STA412H1)

Modern methods of nonparametric inference, with special emphasis on bootstrap methods, and including density estimation, kernel regression, smoothing methods and functional data analysis.
Prerequisite: STA302H1, STA352Y1

STA2111H Graduate Probability I

STA 2111H is a course 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: probability measures, the extension theorem, random variables, distributions, expectations, laws of large numbers, Markov chains.

Students should have a strong undergraduate background in Real Analysis, including calculus, sequences and series, elementary set theory, and epsilon-delta proofs. Some previous exposure to undergraduate-level probability theory is also recommended.

STA2112H Mathematical Statistics I

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

Review of probability theory, distribution theory for normal samples, convergence of random variables, statistical models, sufficiency and ancillarity, statistical functionals,influence curves, maximum likelihood estimation, computational methods.

Prerequisite: Advanced calculus (eg. MAT237) and linear algebra (eg. MAT223, MAT224). A previous course in probability and/or statistics is highly recommended.

STA2162H Statistical Inference I (also offered as undergraduate course STA422H1)

Statistical inference is concerned with using the evidence, available from observed data, to draw inferences about an unknown probability measure. A variety of theoretical approaches have been developed to address this problem and these can lead to quite different inferences. A natural question is then concerned with how one determines and validates appropriate statistical methodology in a given problem. The course considers this larger statistical question. This involves a discussion of topics such as model specification and checking, the likelihood function and likelihood inferences, repeated sampling criteria, loss (utility) functions and optimality, prior specification and checking, Bayesian inferences, principles and axioms, etc. The overall goal of the course is to leave students with an understanding of the different approaches to the theory of statistical inference while developing a critical point-of-view.

Necessary background: Mathematics-based course on the theory of statistics (e.g., at the level of STA352Y).

STA2201H Methods of Applied Statistics II

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.

STA2202H Time Series Analysis (also offered as undergraduate course STA457H1)

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 > ARMA processes, inference and forecasting
  • Non-stationarity and seasonality, ARIMA and SARIMA processes

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

STA2209H Lifetime Data Modeling and Analysis

Students interested in this may wish to take the course, Survival Analysis, offered by the Department of Public Sciences, Biostatistics program.

STA2211H Graduate Probability II

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, and Kolmogorov’s Existence Theorem.

STA2212H Mathematical Statistics II

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

STA2453HY Statistical Consulting

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, an d 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 sta tistics 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.

STA2500H Loss Models (also offered as undergraduate course ACT451H1)

Parametric distributions and transformations, insurance coverage modifications, limits and deductibles, models for claim frequency and severity, models for aggregate claims,stop-loss insurance, risk measures.

Prerequisite: Consult the instructor concerning necessary background for this course

STA2501H Mathematical Risk Theory

Consult the instructor for further details.

Prerequisite: Consult the instructor concerning necessary background for this course

STA2502H Stochastic Methods for Actuarial Science and Finance (also offered as undergraduate course ACT460H1)

This course is an introduction to the stochastic models used in Finance and Actuarial Science. Students will be exposed to the basics of stochastic calculus, particularly focusing on Brownian motions and simple stochastic differential equations. The role that martingales play in the pricing of derivative instruments will be investigated. Some exotic equity derivative products will be explored together with stochastic models for interest rates.

Prerequisite: Knowledge of undergraduate probability theory is necessary. Knowledge of basic financial modeling (e.g., binomial trees and log-normal distributions) is useful, but not completely necessary.

STA2503H Applied Probability for Mathematical Finance

This course features studies in derivative pricing theory and focuses on financial mathematics and its applications to various derivative products. A working knowledge of probability theory, stochastic calculus (see e.g., STA 2502), knowledge of ordinary and partial differential equations and familiarity with the basic financial instruments is assumed. The tentative topics covered in this course include, but is not limited to: no-arbitrage and the fundamental theorem of asset pricing, binomial pricing models; continuous time limits; the Black-Scholes model; the Greeks and hedging; European, American, Asian, barrier and other path-dependent options; short rate models and interest rate derivatives; convertible bonds; stochastic volatility and jumps; volatility derivatives; foreign exchange and commodity derivatives.  Course Website STA 2503

Prerequisite:  Knowledge of undergraduate probability theory is necessary. Knowledge of basic financial modeling (e.g., binomial trees and log-normal distributions), introductory stochastic calculus and financial products is useful, but not necessary. This course moves at a faster pace, is more advanced and contains a higher workload than STA2502, only students who are well prepared will be allowed to take this course. It is also distinct from STA 2047 which instead focuses on the mathematics of stochastic analysis.

 

STA2505H Credibility Theory & Simulation Methods (also offered as undergraduate course ACT466H1)

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

STA2542H Linear Models

This is an advanced graduate course. The emphasis is on linear mixed models and generalized mixed models. Inference requires numerical optimization methods Newton-Raphson and EM algorithms) as well as Monte Carlo sampling methods (importance sampling, accept-reject, Metropolis-Hastings, Gibbs) and these will be taught in class.

Prerequisite: Strong background in Statistics is required.

STA3000Y Advanced Theory of Statistics

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.

STA3431H Monte Carlo Methods

This course will explore Monte Carlo computer algorithms, which use randomness to perform difficult high-dimensional computations. Different types of algorithms, theoretical issues, and practical applications will all be considered. Particular emphasis will be placed on Markov chain Monte Carlo (MCMC) methods. The course will involve a combination of methodological investigations, mathematical analysis, and computer programming.

Prerequisite: Knowledge of statistical inference and probability theory at the advanced undergraduate level, and familiarity with basic computer programming techniques.

 

STA4246H Research Topics in Mathematical Finance

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.

STA4247H Point Processes, noise and stochastic analysis

Introduction to the theory of point processes – Poisson and compound processes, point provesses with repulsion and attraction. Brownian motion, white noise. Stochastic intergration and stochastic differential equtions. Prerequisite: Consult the instructor concerning necessary background for this course

STA4273H Large Scale Machine Learning

Description: Statistical machine learning is a very dynamic field that lies at the intersection of statistics and computational sciences. The goal of statistical machine learning is to develop algorithms that can “learn” from data using statistical and computational methods. Over the last decade, driven by rapid advances in numerous fields, such as computational biology, neuroscience, data mining, signal processing, and finance, applications that involve large amounts of high-dimensional data are not that uncommon.
The goal of this course is to introduce core concepts of large-scale machine learning and discuss scalable techniques for analyzing large amounts of data. Both theoretical and practical aspects will be discussed.

These courses will be streamed using FieldsLive, and students are welcome to attend online. Students interested in obtaining credit for these courses need to arrange with their home department to have them approved as reading or research courses. We will make available the timetable and requirements for the course by September 2014.

STA4412H Topics in Theoretical Statistics Modular Courses

Description: This course will introduce students to the topics under discussion during the thematic program on Statistical Inference in Big Data, with a mix of background lectures and guest lectures. The goal is to prepare students, postdoctoral fellows, and other interested participants to benefit from upcoming workshops in the thematic program, and to provide a venue for further discussion of keynote presentations after the workshops.

These courses will be streamed using FieldsLive, and students are welcome to attend online. Students interested in obtaining credit for these courses need to arrange with their home department to have them approved as reading or research courses. We will make available the timetable and requirements for the course by September 2014.

STA4500H Statistical Dependence: Copula Models and Beyond (0.25 FCE)

The course discusses modern developments in modeling statistical dependence. Emphasis will be placed on copula models, particularly on conditional copula models that can be used in regression settings. Tentative topics include:
– Random Effects
– Copula Models for Continuous Data
– Dependence measures
– Types of Dependence
– Conditional copulas for Continuous Data
– Copula Models for Discrete/Mixed Data
– Conditional Copula Models for Discrete/Mixed Data
– Vines

STA4501H Functional Data Analysis and Related Topics (0.25 FCE)

Functional data analysis (FDA) has received substantial attention in recent years, with applications arising from various disciplines, such as engineering, public health, finance etc. In general, the FDA approaches focus on nonparametric underlying models that often assume the data are observed from realizations of stochastic processes with smooth trajectories. This course will cover general issues in functional data analysis, such as functional principal component analysis, functional regression models, curve clustering and classification. An introduction to smoothing methods will also be included at the beginning of class to provide a basic view of nonparametric regression (kernel and spline types) and serve as the basis of FDA approaches. The course will involve some computing and data analysis using R or matlab.

STA4502H Topics in Stochastic Processes (0.25 FCE)

This course will focus on convergence rates and other mathematical properties of Markov chains on both discrete and general state spaces. Specific methods to be covered will include coupling, minorization conditions, spectral analysis, and more. Applications will be made to card shuffling and to MCMC algorithms.

STA4503H Advanced Monte Carlo Methods and Applications (0.25 FCE)

This course will examine how advanced Monte Carlo methods can be applied to problems in statistical inference. Methods discussed may include use of auxiliary variables, use of Hamiltonian dynamics for Markov chain Monte Carlo updates, use of tempering or annealing to handle multimodal distributions and estimate normalizing constants, and ways of exploiting parallel computation. Practical issues such as verifying that a method has been implemented correctly, assessing convergence of Markov chain methods, assessing the error in estimates, and tuning the parameters of methods will also be discussed. Assignments will involve both the use of available software packages for Monte Carlo estimation and programming of custom methods for particular statistical problems.

STA4504H An Introduction to Bootstrap Methods (0.25 FCE)

The course gives an introduction to some modern methods of nonparametric inference with special emphasis on bootstrap methods. Through a series of data analysis problems involving the bootstrap students are exposed to methods for density estimation, robust and flexible regression. Many fundamental concepts in mathematical statistics are revisited and viewed from the lens of bootstrap simulation providing an important experimental perspective. The course is computationally intensive and requires knowledge of the programming environment R, or some equivalent language. A dominant theme of the course is the expansion of the toolbox of the statistical practitioner through the use of computation in technically complex problems.

STA4505H Applied Stochastic Control : High Frequency and Algorithmic Trading (0.25 FCE)

With the availability of high frequency financial data, new areas of research in stochastic modeling and stochastic control have opened up. This 6 week course will introduce students to the basic concepts, questions and methods that arise in this domain. We will begin with the classical market microstructure models, understand different theories of price formation and price discovery, identify different types of market participants, and then move on to reduced form models. Next, we will investigate some of the typical algorithmic trading strategies employed in industry for different asset classes. Finally, we will develop stochastic optimal control problems for solving optimal liquidation and high frequency market making problems and demonstrate how to solve those problems using the principles of dynamic programming leading to Hamilton-Jacobi-Bellman equations. Students will also have a chance to work with historical limit order book data, develop Monte Carlo simulations and gain a working knowledge of the models and methods. Tentative topics include:
-Market Microstructure
-Overview of Stochastic Calculus
-Dynamic Programming & HJB
-Dynamics of LOB
-Optimal Liquidation
-Market Making
-Risk Measures

STA4506H Non-stationary Time Series Analysis (0.25 FCE)

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.

STA4507H Extreme Value Theory and Applications (0.25 FCE)

Modeling the behaviour of extreme values is important in a variety of disciplines, from finance to environmental science, since catastrophes almost inevitably arise from extreme conditions.  This course will cover both theoretical and applied aspects of extreme value modeling. Some of the topics to be covered are: extreme value types, point process methodology, the Hill and other estimators of the tail index, estimating extreme quantiles, multivariate extremes, estimators of tail dependence.

STA4508H Topics in Likelihood Inference (0.25 FCE)

Inference based on the likelihood function has a prominent role in both theoretical and applied statistics.  This course will introduce some of the more recent developments in likelihood-based inference, with an emphasis on adaptations developed for models with complex structure or large numbers of nuisance parameters.  Special emphasis will be given to the theoretical and applied aspects of composite likelihood, and to the use of quasi-likelihood and generalized estimating equations. Tentative topics to be covered include: review of likelihood inference and asymptotic results; adjustments to profile likelihood; misspecified models — composition likelihood; partially specified models — quasi-likelihood; properties and limitations of penalized likelihood.

STA4509H Insurance Risk Models 1 (0.25 FCE)

The aim of this course is to provide an introduction to advanced insurance risk theory. This course covers frequent and severity models, aggregate losses and compound distributions, EM algorithm, Model selection and estimation.

STA4510H Insurance Risk Models 11 (0.25 FCE)

It covers topics in ruin theory including the classical compound Poisson risk model, ruin probabilities, surplus prior to ruin and deficit at ruin,  connection to queuing models, Gerber-Shiu discounted penalty function, associated integro-differential equation and defective renewal equation, risk models with dividend barrier and dividend strategies.

STA4511H Statistical Issues in Number Theory (0.25 FCE)

We will provide a broad overview of selected areas in analytic number theory (mainly without proofs) leading to a variety of problems and questions involving probability and statistics. The statistical and probabilistic properties of the family of zeta distributions will be discussed in detail. Known and conjectured results about the distribution of (high) primes will be discussed with reference to testing poisson-ness, and applications to testing pseudorandom number generators. The probabilistic heuristic introduced by Cramer (as well as its limitations) will be explored, using such results as the `zero-one laws’ and law of the iterated logarithm. If there is time, statistical properties and modeling of the high zeros of the zeta function will be considered in conjunction with time series and point processes methods.

STA4512H Logical Foundations of Statistical Inference (0.25 FCE)

The general mathematics and logical foundations for statistical inference: geometric, algebraic and topological symmetries that arise naturally in the solution to the inference problem, including rigorous comparison of the bayesian and frequentist approaches, and the group theoretic considerations of invariance (algebraic and logical symmetry), both on the sample space as well as on the parameter space (and both either implicit or manifest) that must be taken into account in the analysis. Unusual for the development, but fundamental to the inherent logic of such considerations, the finite-finite case is given special attention in respect of both sample space and parameter space.

STA4513H Statistical Models of Networks (0.25 FCE)

Our understanding of graph- and network-valued data has undergone a dramatic shift in the past decade. We now understand there to be fundamentally different regimes that relate to the prevalence of edges. The best understood is the dense regime, where, informally speaking, we expect to see edges among vertices chosen uniformly at random from a large graph. The mathematical foundations of this area can be traced back to work by Aldous and Hoover in the early 1980s, but work in graph theory over the past decade has enriched our understanding considerably. Most existing statistical methods, especially Bayesian ones, work implicitly in the dense regime. Real-world networks, however, are not dense. A growing community is now focused on the structure of large sparse graphs. The sparse regime, however, is not well understood: key mathematical notions continue to be identified. We will work through key papers in probability, statistics, and graph theory in order to gain the broader perspective necessary to identify opportunities to contribute to our understanding of statistical methods on graphs and networks.

New! STA4514H  Modelling and Analysis of Spatially Correlated Data (.25 FCE)

This is an advanced course in models and methods for spatial data, with an emphasis on data which are not normally distributed. The course will cover different types of random spatial processes and how to incorporate them into mixed effects models for normal and non-Normal data, with maximum likelihood and Bayesian inference used for the two types of data respectively. Spatial point processes, where dare are random locations rather than measurements at fixed locations, will be dealt with extensively. Following the course, students 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.

New! STA4515H Multiple Hypothesis Testing and its Applications (.25 FCE)

A central issue in many current big-data scientific studies is how to assess statistical significance while taking into account the inherent large-scale multiple hypothesis testing. This 6-week graduate course will first go over the fundamental elements of single and multiple hypothesis testing, then it will move on to more advanced topics such as incorporating prior information to improve power, specific applications to whole genome genetic association studies, as well as discussions of the fallacy of p-value and alternative measures of statistical evidence and significance. Both analytical and empirical arguments will be presented, and participating students are expected to write a research report on suggested or self-selected topics related to multiple hypothesis testing.

New! STA4516H Topics in Probabilistic Programming (.25 FCE)

Probabilistic programming is an emerging area of machine learning, statistics, and computer science, and can be characterized as the systematic study of algorithmic processes that describe and transform uncertainty. Probabilistic programming languages give users the ability to describe complex probabilistic models with code, rather than formulas, while universal inference engines automate the task of implementing inference algorithms for models described by probabilistic code. This class will discuss the key ideas behind probabilistic programming languages and systems, as well as give students a glimpse at the theoretical foundations of probabilistic programming itself.

Pre-Requisites: Mathematical maturity and some background in probability/measure theory, functional programming, and analysis recommended.

Master’s Research Project Course

A limited number of Supervised Research Project courses, normally taken as half-courses, will also be made available, based on faculty availability. These courses will provide students with a first exposure to research-level topics and thinking. Students will normally be required to write a substantial report about their work, plus perhaps give a brief oral presentation. Projects may be proposed either by faculty or by students; information about faculty-proposed projects will be provided in September.

To enroll in such a course, a student must first obtain permission from the supervising faculty member and from the Associate Chair, Graduate Studies. There is no guarantee that enrollment can be provided for all interested students. For further details, please consult the Associate Chair, Graduate Studies.

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