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# Statistical Sciences

### Faculty List

**Professors Emeriti **

D.F. Andrews, M Sc, Ph D

A. Feuerverger, B Sc, Ph D

D.A.S. Fraser, BA, Ph D, FRSC

I. Guttman, MA, Ph D

P. McDunnough, M Sc, Ph D

R. Neal, B Sc, Ph D

M.S. Srivastava, M Sc, Ph D

A.M. Vukov, MA, ASA

**Professor and Chair of the Department **

R. Craiu, B Sc, Ph D

**Professor and Associate Chair, Graduate Studies **

Z. Zhou, B Sc, Ph D

**Assistant Professor, Teaching Stream and Associate Chair, Undergraduate Studies **

V. Zhang, B Sc, M Sc, FSA, ACIA, Actuarial Science

**Associate Professor, Teaching Stream and Associate Chair, Undergraduate Studies **

B. White, Ph D, Statistics

**University Professor **

N.M. Reid, M Sc, Ph D, FRSC, OC

**Professors **

S. Broverman, B Sc, M Sc, Ph D, ASA

R. Craiu, B Sc, Ph D

M.J. Evans, MA, Ph D (UTSC)

S. Jaimungal, B Sc, M Sc, Ph D

K. Knight, M Sc, Ph D

X.S. Lin, M Sc, Ph D, ASA

J. Quastel, MS, Ph D

J.S. Rosenthal, MA, Ph D

J. Stafford, M Sc, Ph D

L. Sun, B Sc. Ph D

B. Virag, Ph D (UTSC)

**Associate Professors **

A. Badescu, B Sc, M Sc, Ph D

D. Brenner M Sc, Ph D

P. Brown, BA, M Sc, Ph D

L.J. Brunner, MA, Ph D (UTM)

Z. Zhou, B Sc, Ph D

**Assistant Professors **

M. Alexander, B Sc, MA, MSR, Ph D

F. Chevalier, B Sc, Ph D

D. Duvenaud, B Sc, M Sc, Ph D

G. Eadie, B Sc, M Sc, Ph D

M. Erdogdu, B Sc, M Sc, Ph D

D. Kong, Ph D (UTM)

D. Roy, B Sc, M Sc, Ph D (UTSC)

S. Pesenti, B Sc, M Sc, Ph D

D. Simpson, Ph D

Q. Sun, Ph D

S. Volgushev, Ph D

L. Wang, B Sc, Ph D

L. Wong, B Sc, M Sc, Ph D

Y. Zhang, B Sc, Ph D

**Professor, Teaching Stream**

A. Gibbs, B Math, B Ed, M Sc, Ph D

**Associate Professor, Teaching Stream **

N. Taback, B Sc, M Sc, Ph D

**Assistant Professors, Teaching Stream**

E. Bolton, Ph D

K. Huynh Wong, B Sc, M Sc

N. Moon, BSc, MA, Ph D

S. Sue-Chee, B Sc, M Sc, Ph D

V. Zhang, B Sc, M Sc, FSA, ACIA

## Introduction

Statistical Science is the science of learning from data. Statistical science plays a large role in data science, which broadly encompasses computational and statistical aspects of managing and learning from large and complex datasets. Statistical theory and methodology have applications in almost all areas of science, social science, public health, medicine, engineering, finance, technology, business, government and industry. Statisticians and data scientists are involved in solving problems as diverse as understanding the health risk of climate change, predicting the path of forest fires, understanding the role of genetics in human health, and creating a better search engine. New ways of collecting, organizing, visualizing, and analyzing data are increasingly driving progress in all fields and have created demand for people with data expertise.

The Department of Statistical Sciences offers specialist, major, and minor programs in Statistics and a specialist program in Data Science. All programs offer training in statistical methods, theory, computation, and communication, as well as an understanding of the role of statistical science to solve problems in a variety of contexts. The specialist program in Statistical Science: Theory and Methods emphasizes probability and statistical theory as underlying mathematical frameworks for data analysis. The specialist program in Statistical Science: Methods and Practice has greater emphasis on collaborative statistical practice. Students in this program combine their study in statistics with a focus in a discipline that relies on statistical methods. The specialist program in Data Science is offered jointly with the Department of Computer Science. Students in this program acquire expertise in statistical reasoning and methods, in the design and analysis of algorithms and data structures for handling big data, in best practices for software design, and in machine learning. The major program in Statistics offers the most flexibility in choice of courses. This program gives students a broad understanding of the methods and computational and communication skills appropriate for effective statistical problem solving. The minor program in Statistics is designed to provide students with exposure and skills in advanced statistical methods.

Enquiries: 100 St. George Street, Sidney Smith Hall, Room 6018 (416-978-3452)

Associate Chair, Undergraduate Studies: Statistics - Associate Professor B. White; e-mail: ugchair.stats@utstat.utoronto.ca

Associate Chair, Undergraduate Studies: Actuarial Science - Professor V. Jiang; e-mail: ugchair.actsci@utstat.utoronto.ca

### Statistical Sciences Programs

### Data Science Specialist (Science Program) - ASSPE1687

**Description:**

The field of Data Science is a combination of statistics and computer science methodologies that enable ‘learning from data’. A data scientist extracts information from data, and is involved with every step that must be taken to achieve this goal, from getting acquainted with the data to communicating the results in non-technical language. The Data Science Specialist program prepares students for work in the Data Science industry or government and for graduate studies in Data Science, Computer Science, or Statistics. Students in the program will benefit from a range of advanced courses in Computer Science and Statistics offered by the University of Toronto, as well as from a sequence of three integrative courses designed especially for the program.

The Data Science Specialist program comprises three fundamental and highly-integrated aspects. First, students will acquire expertise in statistical reasoning, methods, and inference essential for any data analyst. Seconds, students will receive in-depth training in computer science: the design and analysis of algorithms and data structures for handling large amounts of data, and best practices in software design. Students will receive training in machine learning, which lies at the intersection of computer and statistical sciences. The third aspect is the application of computer science and statistics to produce analyses of complex, large-scale datasets, and the communication of the results of these analyses; students will receive training in these areas by taking integrative courses that are designed specifically for the Data Science Specialist program. The courses involve experiential learning: students will be working with real large-scale datasets from the domain of business, government, and/or science. The successful student will combine their expertise in computer and statistical science to produce and communicate analyses of complex large-scale datasets.

Skills that graduates of the program will acquire include proficiency in statistical reasoning and computational thinking; data manipulation and exploration, visualization, and communication that are required for work as a data scientist; the ability to apply statistical methods to solve problems in the context of scientific research, business, and government; familiarity and experience with best practices in software development; and knowledge of current software infrastructure for handling large data sets. Graduates of the program will be able to demonstrate the ability to apply machine learning algorithms to large-scale datasets that arise in scientific research, government, and business; create appropriate data visualizations for complex datasets; identify and answer questions that involve applying statistical methods or machine learning algorithms to complex data, and communicating the results; present theresults and limitations of a data analysis at an appropriate technical level for the intended audience.

**Enrolment Requirements:**

This is a limited enrolment program that can only accommodate a certain number of students. Eligibility is based on the average of a student's grades in CSC148H1 and MAT137Y1/ MAT157Y1 and STA130H1. ( MAT157Y1 grades will be adjusted to account for the course's greater difficulty.)

In addition, students must have completed at least 4.0 FCEs and achieved a minimum grade of 70% in each of CSC148H1, MAT137Y1/ MAT157Y1 and STA130H1.

It is difficult to predict the minimum average required for admission in any given year as it depends on the current capacity of the program and the pool of applicants.

Note that students admitted to the program after second or third year will be required to pay retroactive program fees.

**Completion Requirements:**

(13.0-13.5 Full Course Equivalents [FCEs], including at least 1.5 FCEs at the 400-level)

*First year (3.0 FCEs)*

MAT137Y1/ MAT157Y1; MAT223H1/ MAT240H1 ( MAT240H1 is recommended); STA130H1; CSC108H1; CSC148H1;

Note: Students with a strong background in an object-oriented language such as Python, Java or C++ may omit CSC108H1 and proceed directly with CSC148H1. There is no need to replace the missing half-credit for program completion; however, please base your course choice on what you are ready to take, not on "saving" a half-credit. Consult with the Computer Science Undergraduate Office for advice on choosing between CSC108H1 and CSC148H1.

*Second year (3.5-4.0 FCEs)*

MAT237Y1/ MAT257Y1; STA257H1; STA261H1; CSC207H1; ( CSC165H1, CSC236H1)/ CSC240H1 ( CSC240H1 is recommended); JSC270H1 (Data Science I)

Note: CSC240H1 is an accelerated and enriched version of CSC165H1 plus CSC236H1, intended for students with a strong mathematical background, or who develop an interest after taking CSC165H1. If you take CSC240H1 without CSC165H1, there is no need to replace the missing half-credit for program completion; however, please base your course choice on what you are ready to take, not on "saving" a half-credit. Consult the Computer Science Undergraduate Office for advice on choosing between CSC165H1 and CSC240H1.

*Later years (6.5 FCEs)*

- STA302H1; one of STA303H1 or STA305H1; STA355H1; CSC209H1; CSC263H1/ CSC265H1 ( CSC265H1 is recommended); CSC343H1; CSC373H1; JSC370H1 (Data Science II)
- STA314H1/ CSC311H1/ CSC411H1;
- 2.0 FCEs from the following list, including at least 1.0 FCE at the 400 level (see below for additional conditions): STA303H1/ STA305H1 (whichever one was not taken previously), STA347H1, CSC401H1, STA414H1/ CSC412H1, CSC413H1/ CSC421H1, any 400-level STA course; JSC470H1 (Data Science III).

The choices from 3 must satisfy the requirement for an integrative, inquiry-based activity by including at least 0.5 FCE from the following: JSC470H1 (Data Science III); CSC454H1, CSC490H1, CSC491H1, CSC494H1, CSC495H1, STA490Y1, STA496H1, STA497H1, STA498Y1, STA499Y1. This requirement may also be met by participating in the PEY Co-op (Professional Experience Year Co-op) program.

Students will be advised to develop domain expertise in at least one area where Data Science is applicable, by taking a sequence of courses in that area throughout their program. Examples of such areas will be provided to students by program advisors and will form the basis for a later proposal for program Focuses (to be approved through internal Arts & Science governance procedures).

### Specialist in Statistical Science: Methods and Practice (Science Program) - ASSPE2270

**Description:**

Statistical Science encompasses methods and tools for obtaining knowledge from data and for understanding the uncertainty associated with this knowledge. The purposes of the undergraduate programs are to: (1) equip students with a general framework for obtaining knowledge from data; (2) give students skills that they are able to flexibly apply to a variety of problems; and (3) to provide students with the ability to learn new methods as needs, data sources, and technology change.

The Specialist Program in Statistical Science: Methods and Practice is distinguished from the specialist program in Statistical Science: Theory and Methods through its emphasis on collaborative statistical practice and advanced exposure to an allied discipline. The program includes fundamental concepts in probability and statistical theory with mathematical prerequisites relevant to statistical practice. Students in the program acquire advanced expertise in statistical reasoning, methods, and computation, and complete a concentration in another discipline that permits students to become conversant in that discipline to the extent that they can effectively collaborate. Students will also acquire advanced skills in communication, consultation and collaboration and an understanding of the role of mathematical thinking to support the development and evaluate the properties of statistical methods.

**Enrolment Requirements:**

This is a limited enrolment program that can only accommodate a certain number of students. Eligibility is based on the following:

*For students entering the program after first year:*

A. Completion of at least 4.0 FCEs including:

- STA130H1
- CSC108H1/ CSC120H1/ CSC121H1/ CSC148H1
- MAT223H1/ MAT240H1
- ( MAT135H1, MAT136H1) with a minimum grade of 75% or MAT137Y1 with a minimum grade of 65% or MAT157Y1 with a minimum grade of 65%

AND

B. The average of the grades in STA130H1 and ( MAT135H1, MAT136H1)/ MAT137Y1/ MAT157Y1. Note that students who take ( MAT135H1, MAT136H1) will typically require a higher average grade in these courses than students who take MAT137Y1/ MAT157Y1.

*For students entering the program after 2nd year:*

A. Completion of:

- CSC108H1/ CSC120H1/ CSC121H1/ CSC148H1,
- MAT223H1/ MAT240H1,
- MAT235Y1/ MAT237Y1/ MAT257Y1,
- ( STA237H1, STA238H1) with a minimum grade of 75% or ( STA247H1, STA248H1) with a minimum grade of 75% or ( STA257H1, STA261H1) with a minimum grade of 65%

AND

B. The average of the grades in ( STA237H1, STA238H1)/( STA247H1, STA248H1)/( STA257H1, STA261H1)/ ECO227Y1 and MAT235Y1/ MAT237Y1/ MAT257Y1. Note that students who take ( STA237H1, STA238H1)/( STA247H1, STA248H1) will typically require a higher average grade in these courses than students who took ( STA257H1, STA261H1)/ ECO227Y1.

It is difficult to predict the minimum average required for admission in any given year. More information will be posted on the department website as it becomes available.

**Completion Requirements:**

(10 or 10.5 FCEs plus a disciplinary focus requiring 2.0-3.5 FCEs)

First year:

1. STA130H1, CSC108H1/ CSC120H1/ CSC121H1/ CSC148H1, ( MAT135H1, MAT136H1)/ MAT137Y1/ MAT157Y1. ( MAT137Y1/ MAT157Y1 recommended)

2. Recommended: introductory course in disciplinary focus. MAT223H1/MAT240H1 is also strongly recommended to be taken in first year and is required preparation for MAT237Y1.

Second year:

3. MAT223H1/ MAT240H1, MAT235Y1/ MAT237Y1/ MAT257Y1, ( STA237H1, STA238H1)/( STA247H1, STA248H1)/( STA257H1, STA261H1) (( STA257H1, STA261H1) recommended)

Upper years:

4. STA302H1, STA303H1, STA304H1/ STA305H1, STA314H1/ STA365H1, STA355H1

5. 1.5 FCE from the following list: STA414H1, STA437H1, STA442H1, STA457H1, STA465H1, STA480H1, STA410H1

6. STA490Y1 or successful completion of an internship (see department for information about internships)

7. 1.0 FCE from the following list: MAT224H1/ MAT247H1, MAT337H1/ MAT357H1, CSC148H1, CSC207H1, STA300+ level courses (excluding STA310H5)

**Disciplinary Focuses**

Students in the Specialist Program in Statistical Science: Methods and Practice program must complete at least one disciplinary focus.

To enrol in one or more focuses, students must first be enrolled in the Specialist Program in Statistical Science: Methods and Practice program. Enrolment instructions can be found on the Arts & Science Program Toolkit website. Focuses can be chosen on ACORN after admission to the program, which begins in July.

Health Studies: (2.0 FCE) HST209H1, HST211H1, HST373H1, HST330H1/ HST411H1/ HST464H1

Global Health: (2.5 FCE) BIO120H1, BIO130H1, HMB203H1, HMB323H1, HMB342H1/ HMB433H1 (Recommended: HMB433H1)

Health and Disease: (3.0 FCE) BIO120H1, BIO130H1, HMB202H1, HMB265H1, HMB302H1, HMB321H1/ HMB322H1/ HMB422H1

Fundamental Genetics and its Applications: (3.0 FCE) BIO120H1, BIO130H1, HMB201H1, HMB265H1, HMB301H1, HMB321H1/ HMB421H1/ HMB441H1 (Recommended: HMB421H1)

Neuroscience: (3.5 FCE) BIO120H1, BIO130H1, PSY100H1, HMB200H1/ HMB220H1, HMB265H1, HMB300H1, HMB420H1/ HMB440H1 (Recommended: HMB420H1)

Social Psychology: (2.0 FCE) PSY100H1, PSY220H1, PSY322H1, PSY326H1/ PSY321H1/ PSY424H1/ PSY426H1/ PSY405H1/ PSY406H1

Cognitive Psychology: (2.0 FCE) PSY100H1, PSY270H1, PSY493H1, PSY372H1/ PSY405H1/ PSY406H1/ PSY475H1

Sociolinguistics: (3.0 FCE) LIN100Y1; 2 of LIN228H1, LIN229H1, LIN232H1 or LIN241H1; LIN351H1 and LIN456H1

Psycholinguistics: (3.0 FCE) LIN100Y1; 2 of LIN228H1, LIN229H1, LIN232H1 or LIN241H1; 2 of JLP374H1, JLP315H1 or JLP471H1

Astronomy & Astrophysics: (2.5 or 3.0 FCE) ( PHY131H1, PHY132H1)/( PHY151H1, PHY152H1); AST221H1, AST222H1; ( PHY252H1, AST320H1)/ AST325H1/ AST326Y1

Sociology: (2.5 FCE) SOC100H1+ SOC150H1 (minimum combined average grade of 65%); SOC204H1; 1.0 FCE from SOC303H1, SOC312H1, SOC336H1, SOC355H1, SOC363H1, SOC364H1.

Students interested in advanced study in Sociology should consider additional courses, in particular SOC201H1, SOC251H1, and SOC254H1

Ecology: (3.0 FCE) BIO120H1, BIO220H1; 2.0 FCE from (with at least 0.5 FCE at the 400 level) EEB319H1/ EEB321H1/ EEB328H1/ EEB365H1/ EEB428H1/ EEB433H1/ EEB440H1 or ENV234H1/ ENV334H1/ ENV432H1

Evolutionary Biology: (3.5 FCE) BIO120H1, BIO130H1, BIO220H1; 1.5 FCE from HMB265H1/ BIO260H1, EEB318H1, EEB323H1, EEB324H1, EEB325H1, EEB362H1, EHJ352H1; 0.5 FCE from EEB440H1, EEB455H1, EEB459H1, EEB460H1

Notes:

- BIO260H1 requires BIO230H1 as a prerequisite.
- Students in the Focus in Evolutionary Biology can request that HMB waive the co-requisite of BIO230H1 for HMB265H1 and that EEB waive the prerequisite of BIO230H1 for EEB460H1. These waivers will only be considered for students in the Applied Statistics specialist focus in Evolutionary Biology. All other pre- and co-requisites are required.

Economics: (3.5 FCE) ( ECO101H1, ECO102H1), ECO200Y1/ ECO206Y1, ECO202Y1/ ECO208Y1, 0.5 FCE 300+ series ECO course with the exception of ECO374H1 and ECO375H1

Biochemistry: (3.0 FCE)

CHM135H1, CHM136H1, BCH210H1, BCH311H1, BCH370H1, BCH441H1

Physics: (2.5 FCE)

PHY131H1/ PHY151H1, PHY132H1/ PHY152H1, PHY224H1, PHY252H1/ PHY254H1/ PHY256H1, PHY324H1

Pharmacology and Biomedical Toxicology: (3.0 FCE)

BIO130H1 (minimum grade of 70%), PSL300H1, PSL301H1, PCL201H1, PCL302H1, PCL345H1/ PCL362H1/ PCL469H1/ PCL470H1

### Specialist in Statistical Science: Theory and Methods (Science Program) - ASSPE2290

**Description:**

Statistical Science encompasses methods and tools for obtaining knowledge from data and for understanding the uncertainty associated with this knowledge. The purposes of the undergraduate programs are to: (1) equip students with a general framework for obtaining knowledge from data; (2) give students skills that they are able to flexibly apply to a variety of problems; and (3) to provide students with the ability to learn new methods as needs, data sources, and technology change.

The Specialist Program in Statistical Science: Theory and Methods emphasizes probability and the theory of statistical inference as underlying mathematical frameworks for statistical data analysis. Students in the program acquire advanced expertise in statistical theory and methods, as well as an understanding of the role of statistical science to solve problems in a variety of contexts. The successful student will also acquire skills in mathematical reasoning, computational thinking, and communication in the context of solving statistical problems.

**Enrolment Requirements:**

This is a limited enrolment program that can only accommodate a certain number of students. Eligibility is based on the following:

*For students entering the program after first year:*

1. Completion of at least 4.0 FCEs including:

- STA130H1,
- CSC108H1/ CSC120H1/ CSC121H1/ CSC148H1,
- MAT223H1/ MAT240H1,
- MAT137Y1 with a minimum grade of 65% or MAT157Y1 with a minimum grade of 65%

AND

2. The average of the grades in STA130H1 and MAT137Y1/ MAT157Y1.

*For students entering the program after second year* :

1. Completion of:

- CSC108H1/ CSC120H1/ CSC121H1/ CSC148H1,
- MAT223H1/ MAT240H1,
- MAT237Y1/ MAT257Y1,
- STA257H1 with a minimum grade of 65% and STA261H1 with a minimum grade of 65%

AND

2. The average of the grades in STA257H1 and STA261H1 and MAT237Y1/ MAT257Y1.

It is difficult to predict the minimum average required for admission in any given year. More information will be posted on the department website as it becomes available.

**Completion Requirements:**

(11 full courses or their equivalent)

First Year:

STA130H1, CSC108H1/ CSC120H1/ CSC121H1/ CSC148H1, MAT137Y1/ MAT157Y1, MAT223H1/? MAT240H1

Second Year:

MAT224H1/ MAT247H1, MAT237Y1/ MAT257Y1; STA257H1, STA261H1

Higher Years:

1. STA302H1, STA303H1, STA304H1/ STA305H1, STA314H1/ STA365H1, STA347H1, STA355H1

2. 1.0 FCE from the following list: STA410H1, STA414H1, STA437H1, STA442H1, STA457H1, STA465H1, STA480H1

3. One of STA447H1, STA452H1, STA453H1

4. 1.0 FCE from: ACT451H1, ACT452H1, ACT460H1, MAT327H1, MAT332H1, MAT334H1/ MAT354H1, MAT337H1/ MAT357H1, MAT301H1/ MAT347Y1, MAT344H1, CSC207H1, CSC336H1, CSC343H1, STA300+-level courses (excluding STA310H5)

5. One of STA492H1, STA496H1/ STA497H1/ STA498Y1/ STA499Y1 or successful completion of an internship (see department for more information about internships)

Note: Students planning to take any of these courses should ensure they have the required prerequisites

### Statistics Major (Science Program) - ASMAJ2289

**Description:**

Statistical Science encompasses methods and tools for obtaining knowledge from data and for understanding the uncertainty associated with this knowledge. The purposes of the undergraduate programs are to: (1) equip students with a general framework for obtaining knowledge from data; (2) give students skills that they are able to flexibly apply to a variety of problems; and (3) to provide students with the ability to learn new methods as needs, data sources, and technology change.

The Major in Statistics gives students a broad understanding of the statistical methods and computational and communication skills appropriate for effective statistical problem solving. The successful student will also acquire a general understanding of the role of mathematical thinking to support the development and evaluate the properties of statistical methods. While the Major is designed to complement study in an area of application of quantitative methods, students in the Major may choose to have a greater focus in probability and statistical theory through elective courses.

**Enrolment Requirements:**

*(The following enrolment requirements will be in effect for the 2020 enrolment period.)*

This is a limited enrolment program that can only accommodate a certain number of students. Eligibility is based on the following:

For students entering the program after first year:

A. Completion of at least 4.0 FCEs including:

• STA130H1,

• (MAT135H1, MAT136H1) or MAT137Y1 or MAT157Y1

AND

B. The average of the grades in STA130H1 and ( MAT135H1, MAT136H1)/ MAT137Y1/ MAT157Y1. Note that students who take ( MAT135H1, MAT136H1) will typically require a higher average grade in these courses than students who take MAT137Y1/ MAT157Y1.

For students entering the program after 2nd year:

A. Completion of:

• CSC108H1/ CSC120H1/ CSC121H1/ CSC148H1,

• MAT223H1/ MAT240H1,

• MAT235Y1/ MAT237Y1/ MAT257Y1,

• ( STA237H1, STA238H1) or ( STA247H1, STA248H1) or ( STA257H1, STA261H1) or ECO227Y1

AND

B. The average of the grades in ( STA237H1, STA238H1)/ ( STA247H1, STA248H1)/ ( STA257H1, STA261Y1)/ ECO227Y1 and MAT235Y1/ MAT237Y1/ MAT257Y1. Note that students who take ( STA237H1, STA238H1)/( STA247H1, STA248H1) will typically require a higher average grade in these courses than students who took ( STA257H1, STA261Y1)/ ECO227Y1.

It is difficult to predict the minimum average required for admission in any given year. More information will be posted on the department website as it becomes available.

**Completion Requirements:**

(7.0 full courses or their equivalent, including at least one STA 400-series course)

First Year:

STA130H1, CSC108H1/ CSC120H1/ CSC121H1/ CSC148H1, ( MAT135H1, MAT136H1)/ MAT137Y1/ MAT157Y1.

( MAT223H1/ MAT240H1 recommended in 1st year)

Second Year:

MAT223H1/ MAT240H1, MAT235Y1/ MAT237Y1/ MAT257Y1; ( STA247H1, STA248H1)/( STA237H1, STA238H1)/( STA257H1, STA261H1)/ ECO227Y1

( STA237H1 and STA238H1 are strongly recommended. MAT221H1 may not be used for this requirement.)

Higher Years:

1. STA302H1

2. 0.5 FCE from STA314H1/ STA365H1/ STA347H1/ STA355H1

3. 0.5 FCE from STA414H1/ STA437H1/ STA442H1/ STA457H1/ STA465H1/ STA480H1

4. 1.0 FCE from all available STA300+ level courses, excluding STA310H5

### Statistics Minor (Science Program) - ASMIN2289

**Description:**

Statistical Science encompasses methods and tools for obtaining knowledge from data and for understanding the uncertainty associated with this knowledge.

The Minor in Statistics is designed to provide students with exposure and skills in advanced statistical methods.

**Completion Requirements:**

(4 full courses or their equivalent)

First Year:

MAT133Y1 (70%)/( MAT135H1, MAT136H1)/MAT135Y/ MAT137Y1/ MAT157Y1, CSC108H1/ CSC120H1/ CSC121H1/ CSC148H1 ( MAT135H1, MAT136H1)/ MAT137Y1/ MAT157Y1 is strongly recommended).

STA130H1 is also strongly recommended.

Second Year:

MAT221H1 (70%)/ MAT223H1/ MAT240H1, ( STA220H1/ STA221H1/ ECO220Y1, STA255H1)/( STA237H1, STA238H1)/( STA247H1, STA248H1)/( STA257H1, STA261H1)/ ECO227Y1

MAT221H1 (70%)/ MAT223H1/ MAT240H1 recommended in 1st year

Higher Years:

1 half (H) course equivalent from all available STA300+ level courses (excluding STA310H5)

## About Courses in Statistical Sciences

The statistics course offerings are intended not only for students in statistics programs of study, but also to serve the needs of the many other disciplines that use statistical methods.

- The first year seminar courses, STA198H1 and STA199H1, are designed to provide the opportunity to work closely with an instructor in a small class setting.
- First year students wishing to enrol in a major or specialist program in the Department of Statistical Sciences must take STA130H1, which provides a broad introduction to statistical reasoning, data science, statistical computation and communication.
- The second year foundation courses (STA220H1, STA221H1, STA237H1, STA238H1, STA247H1, STA248H1, STA255H1, STA257H1, and STA261H1) are distinguished primarily by their mathematical demands, as indicated by the prerequisites. Students interested in pursuing more advanced study in probability and theoretical statistics should take STA257H1 and STA261H1. They are the most mathematically rigorous of the 2nd year courses and provide the greatest flexibility when choosing upper-year courses. They are required by students in the specialist programs in Statistical Science: Theory and Methods and Data Science. Students in the specialist program in Statistical Science: Methods and Practice or in the major program in Statistics may instead choose STA237H and STA238H1. Students in computer science programs of study can take STA247H1 and STA248H1. The courses STA288H1, STA220H1 and STA221H1 provide training in statistical reasoning and methods for students in other programs of study, with STA288H1 particularly designed for students in life science programs. Students interested in completing a minor in statistics can combine STA220H1 with STA255H1, which will provide preparation in probability and statistical theory sufficient for many of the upper year courses in statistical methods.
- Pre- and co-requisites are designed to ensure that students have the appropriate preparation for their courses. They are strictly enforced. However, exceptions can be considered for students who have taken an equivalent course at another university. If you have taken courses that are exclusions to pre- or co-requisite courses, though, you should be aware that these are not always equivalent to the requisite courses and may not be allowed.

## Statistical Sciences Courses

### STA130H1 - An Introduction to Statistical Reasoning and Data Science

**Hours:**24L/24P

This course, intended for students considering a program in Statistical Sciences, discusses the crucial role played by statistical reasoning in solving challenging problems from natural science, social science, technology, health care, and public policy, using a combination of logical thinking, mathematics, computer simulation, and oral and written discussion and analysis.

**Corequisite:**MAT135H1/ MAT136H1/ MAT137Y1/ MAT157Y1. Strongly recommended: CSC108H1/ CSC120H1/ CSC121H1/ CSC148H1

**Exclusion:**Any of STA220H1/ STA255H1/ STA248H1/ STA261H1/ ECO220Y1/ ECO227Y1/ STAB22H3/ STA220H5/ STAB57H3/ STA258H5/ STA260H5/ ECO220Y5/ ECO227Y5 taken previously or concurrently

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA198H1 - Probabilities Everywhere

**Hours:**24S

This course examines the meaning and mathematics of probabilities, and how they arise in our everyday lives. Specific topics may include: the nature of coincidences, the concept of luck, games involving dice and cards, long run averages in casinos, margins of error in polls, the interpretation of medical studies, crime statistics, decision making, pseudorandomness, and Monte Carlo algorithms. Restricted to first-year students. Not eligible for CR/NCR option.

**Prerequisite:**Grade 12 Mathematics

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA199H1 - Statistical Evidence: Truth or Myth?

**Hours:**24S

This course explores the impact Statistics has made and continues to make on everyday life through science, law, and the modern methods for information processing. Statistical principles will be illustrated using examples from real life including business, romance and health. Restricted to first-year students. Not eligible for CR/NCR option.

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA201H1 - Why Numbers Matter

**Hours:**36L

This course teaches non-science students the importance of quantitative reasoning to many different areas. It explores a variety of applications to such diverse subjects as economics, gambling, politics, poetry, graphics, music, medicine, demographics, sports, secret codes, and more, using only basic high school level mathematics combined with logical thinking.

**Exclusion:**MAT133Y1/ MAT135H1/ MAT136H1/ MAT137Y1/ MAT157Y1/(MATA32H3, MATA33H3)/(MATA30H3, MATA36H3)/(MATA31H3, MATA37H3)/MAT133Y5/MAT135Y5/MAT137Y5/MAT157Y5. This course is not open to first-year students, nor to students enrolled in any science Major or Specialist program.

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA220H1 - The Practice of Statistics I

**Hours:**36L

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: STA220H1does not count as a distribution requirement course.

**Prerequisite:**Grade 12 Mathematics and one University course in the physical, social, or life sciences

**Exclusion:**ECO220Y1/ ECO227Y1/ GGR270H1/ PSY201H1/ SOC300Y1/ STA250H1/ STA261H1/ STA248H1/ STA288H1/ EEB225H1/ STAB22H3/ STAB57H3/ STA215H5/ STA220H5/ ECO220Y5/ ECO227Y5/ STA258H5/ STA260H5

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA221H1 - The Practice of Statistics II

**Hours:**36L/12T

Continuation of STA220H1 (or similar course), 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).

**Prerequisite:**STA220H1/ STA288H1/ PSY201H1/ GGR270H1/ EEB225H1/STAB22H3/STA220H5

**Exclusion:**ECO220Y1/ ECO227Y1/ GGR270Y1/ PSY202H1/ SOC300H1/ SOC202H1/ SOC252H1/ STA261H1/ STA248H1/ STAB27H3/ STA221H5/ ECO220Y5/ ECO227Y5/ STAB57H3/ STA258H5/ STA260H5

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA237H1 - Probability, Statistics and Data Analysis I

**Hours:**36L/12T

An introduction to probability using simulation and mathematical frameworks, with emphasis on the probability needed for more advanced study in statistical practice. Topics covered include probability spaces, random variables, discrete and continuous probability distributions, probability mass, density, and distribution functions, expectation and variance, independence, conditional probability, the law of large numbers, the central limit theorem, sampling distributions. Computer simulation will be taught and used extensively for calculations and to guide the theoretical development.

**Prerequisite:**( MAT135H1, MAT136H1)/ MAT137Y1/ MAT157Y1/(MATA30H3, MATA36H3)/(MATA31H3, MATA37H3)/MAT135Y5/MAT137Y5/MAT157Y5

**Exclusion:**STA247H1, STA255H1, STA257H1, ECO227Y1, STAB52H3, STA256H5, ECO227Y5

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA238H1 - Probability, Statistics and Data Analysis II

**Hours:**36L/12T

An introduction to statistical inference and practice. Statistical models and parameters, estimators of parameters and their statistical properties, methods of estimation, confidence intervals, hypothesis testing, likelihood function, the linear model. Use of statistical computation for data analysis and simulation.

**Prerequisite:**STA237H1/ STA247H1/ STA257H1/STAB52H3/STA256H5

**Exclusion:**STA248H1, STA255H1, STA261H1, ECO227Y1, STAB57H3, STA258H5, STA260H5, ECO227Y5

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA247H1 - Probability with Computer Applications

**Hours:**36L/12T

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).

**Prerequisite:**( MAT135H1, MAT136H1)/ MAT137Y1/ MAT157Y1/(MATA30H3, MATA36H3)/(MATA31H3, MATA37H3)/MAT135Y5/MAT137Y5/MAT157Y5; CSC108H1/ CSC148H1/CSCA08H3/CSCA48H3/CSC108H5/CSC148H5

**Exclusion:**ECO227Y1/ STA255H1/ STA257H1/STAB52H3/STA256H5/ECO227Y5

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA248H1 - Statistics for Computer Scientists

**Hours:**36L/12T

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).

**Prerequisite:**STA247H1/ STA257H1/STA256H5/STAB52H3; CSC108H1/ CSC148H1/CSCA08H3/CSCA48H3/CSC108H5/CSC148H5

**Exclusion:**ECO220Y1/ ECO227Y1/ GGR270Y1/ PSY201H1/ SOC300H1/ SOC202H1/ SOC252H1/ STA220H1/ STA221H1/ STA250H1/ STA255H1/ STA261H1/ STA288H1/ EEB225H1/ STAB22H3/ STAB27H3/ STAB57H3/ STA220H5/ STA221H5/ STA258H5/ STA260H5/ ECO220Y5/ ECO227Y5

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA255H1 - Statistical Theory

**Hours:**36L/12T

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).

**Prerequisite:**STA220H1/ STA221H1/ ECO220Y1 (note: ECO220Y1 may be taken as a co-requisite)/STAB22H3/STA220H5/ECO220Y5; MAT133Y1 (70%)/( MAT135H1, MAT136H1)/ MAT137Y1/ MAT157Y1/(MATA32H3 (70%), MATA33H3 (70%))/(MATA30H3, MATA36H3)/(MATA31H3, MATA37H3)/MAT133Y5 (70%)/MAT135Y5/MAT137Y5/MAT157Y5

**Exclusion:**ECO227Y1/ STA257H1/ STA261H1/ STA247H1/ STA248H1/STAB52H3/STAB57H3/STA256H5/STA260H5/ECO220Y5

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA257H1 - Probability and Statistics I

**Hours:**36L/12T

A mathematically rigorous introduction to probability, with applications chosen to introduce concepts of statistical inference. Probability and expectation, discrete and continuous random variables and vectors, distribution and density functions, the law of large numbers. The binomial, geometric, Poisson, and normal distributions. The Central Limit Theorem. (Note: STA257H1 does not count as a distribution requirement course).

**Prerequisite:**( MAT135H1 (70%), MAT136H1(70%))/ MAT137Y1/ MAT157Y1 ( MAT137Y1/ MAT157Y1 is strongly recommended)/MATA36H3(70%)/MATA37H3/MAT135Y5(70%)/MAT137Y5/MAT157Y5

**Corequisite:**MAT235Y1/ MAT237Y1/ MAT257Y1 ( MAT237Y1/ MAT257Y1 is strongly recommended)/MATB41H3/MAT232H5/MAT233H5; MAT223H1/ MAT240H1/MATA23H3/MAT223H5/MAT240H5

**Exclusion:**ECO227Y1, STA247H1, MAT377H1, STAB52H3, STA256H5, ECO227Y5

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA261H1 - Probability and Statistics II

**Hours:**36L/12T

A rigourous introduction to the theory of statistical inference and to statistical practice. Statistical models, parameters, and samples. Estimators for parameters, sampling distributions for estimators, and the properties of consistency, bias, and variance. The likelihood function and the maximum likelihood estimator. Hypothesis tests and confidence regions. Examples illustrating statistical theory and its limitations. Introduction to the use of a computer environment for statistical analysis. (Note: STA261H1 does not count as a distribution requirement course).

**Prerequisite:**STA257H1/STAB52H3/STA256H5

**Corequisite:**MAT235Y1/ MAT237Y1/ MAT257Y1/MATB42H3/MAT236H5; MAT223H1/ MAT240H1/MATA23H3/MAT223H5/MAT240H5

**Exclusion:**ECO227Y1/ STA248H1/ STA255H1/STAB57H3/STA260H5/ECO227Y5

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### JSC270H1 - Data Science I

**Hours:**24L/24P

This course is restricted to students in the Data Science Specialist program. Data exploration and preparation; data visualization and presentation; and computing with data will be introduced. Professional skills, such as oral and written communication, and ethical skills for data science will be introduced. Data science workflows will be integrated throughout the course. These topics will be explored through case studies and collaboration with researchers in other fields.

**Prerequisite:**STA257H1, CSC207H1

**Corequisite:**STA261H1, MAT237Y1/ MAT257Y1, CSC236H1/ CSC240H1

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA288H1 - Statistics and Scientific Inquiry in the Life Sciences

**Hours:**36L/18P

Introduction to statistics and its connection to all stages of the scientific inquiry process. Issues around data collection, analysis and interpretation are emphasized to inform study design and critical assessment of published research. Statistical software is used to conduct descriptive and inferential statistics to address basic life sciences research questions.

**Prerequisite:**BIO230H1/ BIO255H1

**Exclusion:**STA220H1, PSY201H1, GGR270H1, ECO220Y1, ECO227Y1, SOC202H1, EEB225H1, HMB325H1, STA248H1, STA261H1, PCL376H1, STA215H5, STA220H5, STAB22H3

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA299Y1 - Research Opportunity Program

**Hours:**TBA

Credit course for supervised participation in faculty research project. Details at http://www.artsci.utoronto.ca/current/course/rop. Not eligible for CR/NCR option.

**Distribution Requirements:**Science

### STA302H1 - Methods of Data Analysis I

**Hours:**36L

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/STAB57H3/STA258H5/STA260H5/ECO227Y5; CSC108H1/ CSC120H1/ CSC121H1/ CSC148H1/CSCA08H3/CSCA48H3/CSC108H5/CSC148H5; MAT221H1(70%)/ MAT223H1/ MAT240H1/MATA23H3/MAT223H5/MAT240H5

**Exclusion:**STAC67H3, STA302H5

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA303H1 - Methods of Data Analysis II

**Hours:**36L

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

**Prerequisite:**STA302H1/STAC67H3/STA302H5

**Exclusion:**STAC51H3

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA304H1 - Surveys, Sampling and Observational Data

**Hours:**36L

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.

**Prerequisite:**ECO220Y1/ ECO227Y1/ GGR270H1/ PSY201H1/ SOC300H1/ SOC202H1/ STA220H1/ STA255H1/ STA261H1/ STA248H1/ STA238H1/ STA288H1/ EEB225H1/ STAB22H3/ STAB57H3/ STA220H5/ STA258H5/ STA260H5/ ECO220Y5/ ECO227Y5

**Exclusion:**STAC50H3, STAC52H3, STA304H5

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA305H1 - Design and Analysis of Experiments

**Hours:**36L

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.

**Prerequisite:**STA302H1/STAC67H3/STA302H5

**Exclusion:**STAC50H3, STAC52H3, STA305H5

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA314H1 - Statistical Methods for Machine Learning I

**Hours:**36L/12T

Statistical methods for supervised and unsupervised learning from data: training error, test error and cross-validation; classification, regression, and logistic regression; principal components analysis; stochastic gradient descent; decision trees and random forests; k-means clustering and nearest neighbour methods. Computational tutorials will support the efficient application of these methods.

**Prerequisite:**STA238H1/ STA248H1/ STA255H1/ STA261H1/STAB57H3/STA260H5; CSC108H1/ CSC120H1/ CSC121H1/ CSC148H1/CSCA08H3/CSCA48H3/CSCA20H3/CSC108H5/CSC148H5; MAT223H1/ MAT240H1/MATA23H3/MAT223H5/MAT240H5; MAT235Y1/ MAT237Y1/ MAT257Y1/(MATB41H3, MATB42H3)/(MAT232H5, MAT236H5)/(MAT233H5, MAT236H5)

**Corequisite:**STA302H1/STA302H5

**Exclusion:**CSC411H1, CSC311H1, STA314H5, STA315H5, CSCC11H3, CSC411H5

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA347H1 - Probability

**Hours:**36L

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.

**Prerequisite:**STA247H1/ STA255H1(70%)/ STA237H1(70%)/ STA257H1/ ECO227Y1/STAB52H3/STA256H5; MAT223H1/ MAT240H1/MATA23H3/MAT223H5/MAT240H5; MAT235Y1/ MAT237Y1/ MAT257Y1/(MATB41H3, MATB42H3)/(MAT232H5, MAT236H5)/(MAT233H5, MAT236H5) (Note: STA257H1, MAT223H1/ MAT240H1, MAT237Y1/ MAT257Y1 are very strongly recommended)

**Exclusion:**MAT377H1/STAC62H3

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA355H1 - Theory of Statistical Practice

**Hours:**24L/12P

STA355H1 provides a unifying structure for the methods taught in other courses, and will enable students to read methodological research articles or articles with a large methodological component. Topics covered include statistical models and distributions; fundamentals of inference: estimation, hypothesis testing, and significance levels; likelihood functions and likelihood-based inference; prior distributions and Bayesian inference.

**Prerequisite:**STA255H1 (75%)/ STA248H1 (75%)/ STA238H1 (75%)/ STA261H1 (60%)/ ECO227Y1 (60%)/STAB57H5 (60%)/STA260H5 (60%)/ECO227Y5 (60%); MAT235Y1/ MAT237Y1/ MAT257Y1/(MATB41H3, MATB42H3)/(MAT232H5, MAT236H5)/(MAT233H5, MAT236H5); MAT223H1/ MAT240H1/MATA23H3/MAT223H5/MAT240H5

**Exclusion:**STAC58H3

**Recommended Preparation:**CSC108H1/ CSC120H1/ CSC121H1/ CSC148H1

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA365H1 - Applied Bayesian Statistics

**Hours:**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/STAC67H3/STA302H5

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### JSC370H1 - Data Science II

**Hours:**24L/24P

This course is restricted to students in the Data Science Specialist program. Students will learn to identify and answer questions through the application of exploratory data analysis, data visualization, statistical methods or machine learning algorithms to complex data. Software development for data science and reproducible workflows. Communication of statistical information at various technical levels, ethical practice of data analysis and software development, and teamwork skills. Topics will be explored through case studies and collaboration with researchers in other fields.

**Prerequisite:**JSC270H1, STA261H1, MAT237Y1/ MAT257Y1, CSC263H1, STA302H1, CSC343H1

**Corequisite:**STA303H1/ STA305H1

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA398H0 - Research Excursions

**Hours:**TBA

An instructor-supervised group project in an off-campus setting. Details at http://www.artsci.utoronto.ca/current/course/rep. Not eligible for CR/NCR option.

**Distribution Requirements:**Science

### STA398Y0 - Research Excursions

**Hours:**TBA

An instructor-supervised group project in an off-campus setting. Details at http://www.artsci.utoronto.ca/current/course/rep. Not eligible for CR/NCR option.

**Distribution Requirements:**Science

### STA399Y1 - Research Opportunity Program

**Hours:**TBA

Credit course for supervised participation in faculty research project. Details at http://www.artsci.utoronto.ca/current/course/rop. Not eligible for CR/NCR option.

### STA410H1 - Statistical Computation

**Hours:**36L

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.

**Prerequisite:**STA302H1/STAC67H3/STA302H5; CSC108H1/ CSC120H1/ CSC121H1/ CSC148H1/CSCA08H3/CSCA48H3/CSCA20H3/CSC108H5/CSC148H5; MAT223H1/ MAT240H1/MATA23H3/MAT223H5/MAT240H5

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA414H1 - Statistical Methods for Machine Learning II

**Hours:**36L

Probabilistic foundations of supervised and unsupervised learning methods such as naive Bayes, mixture models, and logistic regression. Gradient-based fitting of composite models including neural nets. Exact inference, stochastic variational inference, and Marko chain Monte Carlo. Variational autoencoders and generative adversarial networks.

**Prerequisite:**STA314H1/ CSC411H1/ CSC311H1/(STA314H5, STA315H5)/CSCC11H3/CSC411H5; STA302H1/STAC67H3/STA302H5; CSC108H1/ CSC120H1/ CSC121H1/ CSC148H1/CSCA08H3/CSCA48H3/CSCA20H3/CSC108H5/CSC148H5; MAT235Y1/ MAT237Y1/ MAT257Y1/(MATB41H3, MATB42H3)/(MAT232H5, MAT236H5)/(MAT233H5, MAT236H5); MAT223H1/ MAT240H1/MATA23H3/MAT223H5/MAT240H5

**Exclusion:**CSC412H1

**Recommended Preparation:**STA303H1

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA422H1 - Theory of Statistical Inference

**Hours:**36L

This course examines current theory of statistical inference, particularly likehood-based methods and Bayesian methods with an emphasis on resolving present conflicts; log-model expansion and asymptotics are primary tools.

**Prerequisite:**STA355H1

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA437H1 - Methods for Multivariate Data

**Hours:**24L/12P

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.

**Prerequisite:**STA302H1/ STA352Y1/STAC67H3/STA302H5 ( MAT224H1/ MAT247H1 recommended)

**Exclusion:**STAD37H3, STA437H5

**Recommended Preparation:**MAT223H1/ MAT240H1/

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA442H1 - Methods of Applied Statistics

**Hours:**36L

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.

**Prerequisite:**STA302H1/STAC67H3/STA302H5; CSC108H1/ CSC120H1/ CSC121H1/ CSC148H1/CSCA08H3/CSCA48H3/CSCA20H3/CSC108H5/CSC148H5

**Exclusion:**STA441H5

**Recommended Preparation:**At least an additional 1.0 FCE in STA courses at the 300 or 400 level

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA447H1 - Stochastic Processes

**Hours:**36L

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:**STA347H1/ MAT377H1/STAC62H3

**Exclusion:**STA348H5, STAC63H5

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA450H1 - Topics in Statistics

**Hours:**36L

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.

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA452H1 - Mathematical Statistics I

**Previous Course Number:**STA352Y1

**Hours:**36L

Statistical theory and its applications at an advanced mathematical level. Topics include probability and distribution theory as it specifically pertains to the statistical analysis of data. Linear models and the geometry of data, least squares and the connection to conditional expectation. The basic concept of inference and the likelihood function.

**Prerequisite:**MAT223H1/ MAT240H1/MATA23H3/MAT223H5/MAT240H5; MAT235Y1/ MAT237Y1/ MAT257Y1/(MATB41H3, MATB42H3)/(MAT232H5, MAT236H5)/(MAT233H5, MAT236H5); ( STA257H1, STA355H1)/ STA347H1. Note: MAT237Y1/ MAT257Y1; ( MAT223H1, MAT224H1)/ MAT240H1 very strongly recommended.

**Exclusion:**STA352Y1

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA453H1 - Mathematical Statistics II

**Previous Course Number:**STA352Y1

**Hours:**36L

Continuation of STA452H1: statistical theory and its applications at an advanced mathematical level. Topics include classical estimation, theory with methods based on the likelihood function and the likelihood statistics. Testing hypothesis and the evaluation of conference from both a bayesian and frequentist point of view.

**Prerequisite:**STA452H1

**Exclusion:**STA352Y1

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA457H1 - Time Series Analysis

**Hours:**36L

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.

**Prerequisite:**STA302H1/STAC67H3/STA302H5; MAT235Y1/ MAT237Y1/ MAT257Y1/(MATB41H3, MATB42H3)/(MAT232H5, MAT236H5)/(MAT233H5, MAT236H5)

**Exclusion:**STAD57H3, STA457H5

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA465H1 - Theory and Methods for Complex Spatial Data

**Hours:**36L

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.

**Prerequisite:**STA302H1/STAC67H3/STA302H5, STA303H1

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### JSC470H1 - Data Science III

**Hours:**24L/24P

This course is **restricted to** students in the Data Science Specialist program. Research topics and applications of data science methods will be explored through case studies and collaboration with researchers in other fields. Data analysis, visualization, and communication of statistical information at various technical levels, ethical practice of data analysis and software development, and teamwork skills.

**Prerequisite:**JSC370H1, STA314H1/ CSC411H1/ CSC311H1, STA303H1/ STA305H1

**Exclusion:**STA490Y1

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA480H1 - Fundamentals of Statistical Genetics

**Hours:**36L/9P

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.

**Prerequisite:**STA303H1

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA490Y1 - Statistical Consultation, Communication, and Collaboration

**Previous Course Number:**STA490H1

**Hours:**48L/48P

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.

**Prerequisite:**STA303H1, STA304H1/ STA305H1, STA355H1 (Permission of instructor. Priority is given to students completing all requirements of the Applied Statistics specialist program.)

**Corequisite:**one additional 400 level STA course

**Exclusion:**STA490H1

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA492H1 - Seminar in Statistical Science

**Hours:**36S

This course is intended for students completing the Statistical Science: Theory and Methods Specialist program. Novel influential ideas and current research topics in statistics will be explored through readings and discussion. Content will generally vary from semester to semester. Student presentations and written reports will be required.

**Prerequisite:**STA355H1 (Permission of instructor. Priority is given to students completing all requirements of the Statistical Science: Theory and Methods specialist program.)

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA496H1 - Readings in Statistics

**Hours:**TBA

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. Not eligible for CR/NCR option.

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA497H1 - Readings in Statistics

**Hours:**TBA

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. Not eligible for CR/NCR option.

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA498Y1 - Readings in Statistics

**Hours:**TBA

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. Not eligible for CR/NCR option.

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)

### STA499Y1 - Readings in Statistics

**Hours:**TBA

**Distribution Requirements:**Science

**Breadth Requirements:**The Physical and Mathematical Universes (5)