Faculty of Arts & Science 2011-2012 Calendar

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Statistics

Faculty

Statistical methods have applications in almost all areas of science, engineering, business, government, and industry. The practising statistician is involved in such diverse projects as designing clinical trials to test a new drug, economic model-building to evaluate the costs of a guaranteed-income scheme, predicting the outcome of a national election, planning a survey of television viewing habits, and estimating animal populations.

Today’s consumer is bombarded with the results of so many quantitative studies using statistical methodology that it is necessary to know something about statistics in order to be properly critical. A basic knowledge of statistics should be an integral part of everyone’s general education.

Probability theory is used to analyse the changing balance among the age-groups in a population as the birth rate changes, the control force needed to keep an aircraft on course through gusts of wind, the chance that the demand for electricity by all the customers served by a substation will exceed its capacity. These are just three of many phenomena that can be analysed in terms of randomness and probability.

The course offerings are intended not only for specialists in the theory of the subject but also to serve the needs of the many other disciplines that use statistical methods, e.g. in sample survey design and experimental design. Students following the Specialist Program are encouraged to include courses in major fields of application in their overall program. The Major Program can be profitably combined with specialization in another discipline. Students in these programs may also qualify for the A. Stat. designation from the Statistical Society of Canada.

Both applied and theoretical courses are offered in Statistics and Probability. The foundation courses STA220H1, STA221H1, STA247H1, STA248H1, STA250H1, STA255H1, STA257H1, and STA261H1 are distinguished primarily by their mathematical demands, as indicated by the prerequisites. Students interested in the Biological or Social Sciences will generally find the most relevant courses of the more advanced offerings to be STA302H1, STA303H1, STA304H1, STA305H1 and STA429H1. Furthermore, the probability course STA347H1 will be of interest to those whose field of application includes stochastic models.

Enquiries: 100 St. George Street, Sidney Smith Hall, Room 6022 (416-978-5136)

Associate Chair, Undergraduate Studies: Professor D. Brenner; e-mail: brenner@utstat.utoronto.ca

Associate Chair, Undergraduate Studies: Actuarial Science – Professor S Broverman; e-mail: sam@utstat.utoronto.ca

Statistics Programs

Enrolment in this program requires the completion of 4.0 courses.

(11 full courses or their equivalent)

First Year:
CSC148H1/CSC260H1; MAT137Y1/MAT157Y1

Second Year:
MAT223H1/MAT240H1, MAT224H1/MAT247H1, MAT237Y1/MAT257Y1; STA257H1, STA261H1
(MAT223H1/MAT240H1 recommended in 1st year) while CSC148H1/CSC260H1 might well be taken in 2nd year)

Higher Years:
1. STA302H1, STA303H1, STA347H1, STA352Y1, STA410H1, STA442H1
2. 1.5 full year courses from: STA412H1, (STA414H1/CSC411H1), STA422H1, STA437H1, CSC438H1, CSC447H1, CSC457H1
3. 1.5 full year courses from: ACT451H1, ACT452H1, ACT460H1; APM412H1;
MAT327H1, MAT334H1/MAT354H1, MAT337H1/MAT357H1, MAT301H1/MAT347Y1
CSC207H1, CSC310H1, CSC336H1/CSC350H1, CSC351H1
STA300 + level courses

Enrolment in this program requires the completion of 4.0 courses.

(6.5 full courses or their equivalent, including at least one STA400-series course)

First Year:
CSC108H1/CSC148H1/CSC260H1 (may be taken in 2nd year); MAT135Y1/MAT137Y1/MAT157Y1

Second Year:
MAT223H1/MAT240H1, MAT235Y1/MAT237Y1/MAT257Y1; (STA250H1, STA255H1)/(STA247H1, STA248H1)/(STA257H1, STA261H1)(MAT223H1/MAT240H1 recommended in 1st year)

Higher Years:
1. STA302H1
2. 3 half (H) course equivalents from all available STA300+ level courses (For example, a student interested in economics/commerce/finance might think to include STA304H1, STA347H1, STA457H1 in their programme, while someone engaged in a life science might entertain STA303H1, STA305H1, STA437H1. On the other hand, a student with an interest in pure math might choose to focus on applications of that subject matter to theoretical probability and statistics, selecting STA347H1, STA352Y1 and447H1 to complete a major in statistics.)
3. 1 half (H) course equivalent from the available STA400+ level courses (For those anticipating a future professional need to analyze large arrays of data STA410H1, STA414H1 are certainly very worthy of consideration.)

Enrolment in this program requires the completion of 4.0 courses.

(4 full courses or their equivalent)

First Year:
MAT135Y1/MAT137Y1/MAT157H1

Second Year:
MAT223H1/MAT240H1; (STA250H1/STA220H1 (70%), STA255H1)/(STA247H1, STA248H1)/(STA257H1, STA261H1)
(MAT223H1/MAT240H1 recommended in 1st year)

Higher Years:
STA302H1
2. 2 half (H) course equivalents from all available STA300+ level courses

Enrolment in this program requires the completion of 4.0 courses.

(11 full courses or their equivalent)

First Year:
MAT157Y1, MAT240H1

Second Year:
MAT247H1, MAT257Y1, MAT267H1; STA257H1; STA261H1

Third and Fourth Years:
1. MAT327H1, MAT354H1, MAT357H1; STA302H1, STA352Y1, STA347H1, STA447H1
2. At least three half-courses from STA303H1, STA305H1, STA410H1, STA414H1, STA422H1, STA437H1, STA438H1, STA442H1, STA450H1, STA457H1
3. At least one 300+ level f.c.e. from APM, CSC, MAT

Note
The Department recommends that PHY151H1, PHY152H1 be taken in first year, and that CSC108H1/CSC148H1/CSC260H1 be taken during the program

Statistics Courses

The 199Y1 and 199H1 seminars are designed to provide the opportunity to work closely with an instructor in a class of no more than twenty-four students. These interactive seminars are intended to stimulate the students’ curiosity and provide an opportunity to get to know a member of the professorial staff in a seminar environment during the first year of study. Details here.

An introductory course in statistical concepts and methods, emphasizing exploratory data analysis for univariate and bivariate data, sampling and experimental designs, basic probability models, estimation and tests of hypothesis in one-sample and comparative two-sample studies. A statistical computing package is used but no prior computing experience is assumed. (Note: STA220H1 does not count as a distribution requirement course)

Continuation of STA220H1, emphasizing major methods of data analysis such as analysis of variance for one factor and multiple factor designs, regression models, categorical and non-parametric methods (Note: STA221H1 does not count as a distribution requirement course).

Introduction to the theory of probability, with emphasis on applications in computer science. The topics covered include random variables, discrete and continuous probability distributions, expectation and variance, independence, conditional probability, normal, exponential, binomial, and Poisson distributions, the central limit theorem, sampling distributions, estimation and testing, applications to the analysis of algorithms, and simulating systems such as queues (Note: STA247H1 does not count as a distribution requirement course).

A survey of statistical methodology with emphasis on data analysis and applications. The topics covered include descriptive statistics, data collection and the design of experiments, univariate and multivariate design, tests of significance and confidence intervals, power, multiple regression and the analysis of variance, and count data. Students learn to use a statistical computer package as part of the course (Note: STA248H1 does not count as a distribution requirement course).

A survey of statistical methodology with emphasis on data analysis and applications. The topics covered include descriptive statistics, basic probability, simulation, data collection and the design of experiments, tests of significance and confidence intervals, power, multiple regression and the analysis of variance, and count data. Students learn to use a statistical computer package as part of the course (Note: STA250H1 does not count as a distribution requirement course).

This courses deals with the mathematical aspects of some of the topics discussed in STA250H1. Topics include discrete and continuous probability distributions, conditional probability, expectation, sampling distributions, estimation and testing, the linear model (Note: STA255H1 does not count as a distribution requirement course).

This course, and its sequel, STA261H1, are mathematically quite challenging, the target audience  includes anyone proceeding directly to a specialist degree in statistics, as well as anyone with serious and special interest in some other of the identifiably statistical-physical sciences.  Topics, albeit very rigorously covered, are, nevertheless, very standard introductory ones: abstract probability and expectation, discrete and continuous random variables and vectors, with the special mathematics of distribution and density functions, all realized in the special examples of ordinary statistical practice: the binomial, poisson and geometric group, and the gaussian (normal), gamma, chi-squared complex.

A sequel to STA257H1, providing a rigorous introduction to the logical foundations of statistical inference and the practical methodology engendered. Topics include: statistical models, parameters, samples and estimates; the general concept of statistical confidence with applications to the discrete case and the construction of confidence intervals and more general regions in both the univariate and vector-valued cases; hypothesis testing; the likelihood function and its applications; time permitting: the basics of data analysis, unbiasedness, sufficiency, linear models and regression (Note: STA261H1 does not count as a distribution requirement course).

Credit course for supervised participation in faculty research project. Details here.

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.

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

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.

Experiments vs observational studies, experimental units. Designs with one source of variation. Complete randomized designs and randomized block designs. Factorial designs. Inferences for contrasts and means. Model assumptions. Crossed and nested treatment factors, random effects models. Analysis of variance and covariance. Sample size calculations.

An overview of probability from a non-measure theoretic point of view. Random variables/vectors; independence, conditional expectation/probability and consequences. Various types of convergence leading to proofs of the major theorems in basic probability. An introduction to simple stochastic processes such as Poisson and branching processes.

Introduction to statistical theory and its application. Basic inference concepts. Likelihood function, Likelihood statistic. Simple large sample theory. Least squares and generalizations, survey of estimation methods. Testing hypotheses, p-values and confidence intervals. Bayesian-frequentist interface. Analysis of variance, conditional inference.

Prerequisite: MAT223H1/MAT240H1; MAT235Y1/MAT237Y1/MAT257Y1; (STA257H1,STA261H1)/ECO227Y1 Note: MAT237Y1/MAT257Y1; (MAT223H1, MAT224H1)/MAT240H1 very strongly recommended.
Distribution Requirement Status: This is a Science course
Breadth Requirement: The Physical and Mathematical Universes (5)

STA365H1 Applied Bayesian Statistics [36L]

Bayesian inference has become an important applied technique and is especially valued to solve complex problems. This course first examines the basics of Bayesian inference. From there, this course looks at modern, computational methods and how to make inferences on complex data problems.

Prerequisite: STA302H1
Distribution Requirement Status: This is a Science course
Breadth Requirement: The Physical and Mathematical Universes (5)

STA398H0    Independent Experiential Study Project

An instructor-supervised group project in an off-campus setting. Details here.

An instructor-supervised group project in an off-campus setting. Details here.

Programming in an interactive statistical environment. Generating random variates and evaluating statistical methods by simulation. Algorithms for linear models, maximum likelihood estimation, and Bayesian inference. Statistical algorithms such as the Kalman filter and the EM algorithm. Graphical display of data.

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

Statistical aspects of supervised learning: regression with spline bases, regularization methods, parametric and nonparametric classification methods, nearest neighbours, cross-validation and model selection, generalized additive models, trees, model averaging, clustering and nearest neighbour methods for unsupervised learning.

The course discusses foundational aspects of various theories of statistics. Specific topics covered include: likelihood based inference, decision theory, fiducial and structural inference, Bayesian inference.

The course discusses many advanced statistical methods used in the life and social sciences. Emphasis is on learning how to become a critical interpreter of these methodologies while keeping mathematical requirements low. Topics covered include multiple regression, logistic regression, discriminant and cluster analysis, principal components and factor analysis.

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 partial, multiple and canonical correlations; multivariate analysis of variance; profile analysis and curve fitting for repeated measurements; classification and the linear discriminant function.

An introductory survey of current multivariate analysis, multivariate normal distributions, distribution of multiple and partial correlations, Wishart distributions, distribution of Hotellings T2, testing and estimation of regression parameters, classification and discrimination.

Advanced topics in statistics and data analysis with emphasis on applications. Diagnostics and residuals in linear models, introduction to generalized linear models, graphical methods, additional topics such as random effects models, designed experiments, model selection,  analysis of censored data, introduced as needed in the context of case studies.

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).

Topics of current research interest are covered. Topics change from year to year, and students should consult the department for information on material presented in a given year.

An overview of methods and problems in the analysis of time series data. Topics include: descriptive methods, filtering and smoothing time series, theory of stationary processes, identification and estimation of time series models, forecasting, seasonal adjustment, spectral estimation, bivariate time series models.

Through case studies and collaboration with researchers in other disciplines, students develop skills in the collaborative practice of Statistics. Focus is on pragmatic solutions to practical issues including study design, dealing with common complications in data analysis, and ethical practice, with particular emphasis on written communication.

Independent study under the direction of a faculty member. Persons wishing to take this course must have the permission of the Undergraduate Secretary and of the prospective supervisor.

Independent study under the direction of a faculty member. Persons wishing to take this course must have the permission of the Undergraduate Secretary and of the prospective supervisor.

Independent study under the direction of a faculty member. Persons wishing to take this course must have the permission of the Undergraduate Secretary and of the prospective supervisor.

Independent study under the direction of a faculty member. Persons wishing to take this course must have the permission of the Undergraduate Secretary and of the prospective supervisor.