# Graduate Course Descriptions

## Regular courses

Each course title links to the official course catalog entry in myPurdue. Consult myPurdue for additional information.

**STAT 50100 - ** Experimental Statistics I

Concepts and methods of applied statistics. Exploratory analysis of data. Sample design and experimental design. Normal distributions. Sampling distributions. Confidence intervals and tests of hypotheses for one and two samples. Inference for contingency tables, regression and correlation, and one-way analysis of variance. Use of the SAS statistical software. Intended primarily for students who have not had calculus. Not open to students in mathematical sciences or engineering. For statistics majors and minors, credit should be allowed in no more than one of STAT 30100, STAT 35000, STAT 50100, and in no more than one of STAT 50300 and STAT 51100. Prerequisite: College Algebra. Typically offered Fall, Spring, Summer. 3.0 credit hours.

**STAT 50200 -** Experimental Statistics II

Regression with several explanatory variables. Regression diagnostics. Analysis of variance for factorial designs. Multiple comparisons. Analysis of covariance. Repeated measures designs. Extensive use of the SAS statistical software. Intended primarily for students who have not had calculus. Not open to students in mathematical sciences or engineering. Typically offered Summer and Spring. 3.0 credit hours.

**STAT 50300 -** Statistical Methods for Biology

Introductory statistical methods, with emphasis on applications in biology. Topics include descriptive statistics, binomial and normal distributions, confidence interval estimation, hypothesis testing, analysis of variance, introduction to nonparametric testing, linear regression and correlation, goodness-of-fit tests, and contingency tables. Open only to majors related to the life sciences. For statistics majors and minors, credit should be allowed in no more than one of STAT 30100, STAT 35000, STAT 50100, and in no more than one of STAT 50300 and STAT 51100. Typically offered Fall, Spring, Summer. 3.0 credit hours.

**STAT 50600 -** Statistical Programming and Data Management

Use of the SAS software system for managing statistical data. The SAS environment. Data description. Data access and management. SAS macro language and application development. Prerequisite: STAT 51200 and coursework in computer programming. Typically offered Fall and Spring. 3.0 credit hours.

**STAT 51100 -** Statistical Methods

Descriptive statistics; elementary probability; sampling distributions; inference, testing hypotheses, and estimation; normal, binomial, Poisson, hypergeometric distributions; one-way analysis of variance; contingency tables; regression. For statistics majors and minors, credit should be allowed in no more than one of STAT 30100, STAT 35000, STAT 50100, and in no more than one of STAT 50300 and STAT 51100. Prerequisite: Two semesters of college calculus. Typically offered Fall and Spring. 3.0 credit hours.

**STAT 51200 -** Applied Regression Analysis

Inference in simple and multiple linear regression, residual analysis, transformations, polynomial regression, model building with real data, nonlinear regression. One-way and two-way analysis of variance, multiple comparisons, fixed and random factors, analysis of covariance. Use of existing statistical computer programs. Prerequisite: Coursework in Statistical Methods with a calculus prerequisite. Typically offered Fall, Spring, and Summer. 0.0 or 3.0 credit hours.

**STAT 51300** - Statistical Quality Control

A strong background in control charts including adaptations, acceptance sampling for attributes and variables data, standard acceptance plans, sequential analysis, statistics of combinations, moments and probability distributions, applications. Typically offered Fall and Spring. 3.0 credit hours.

**STAT 51400 - ** Design of Experiments

Fundamentals, completely randomized design; randomized complete blocks; latin square; multi-classification; factorial; nested factorial; incomplete block and fractional replications for 2n, 3n, 2m x 3n; confounding; lattice designs; general mixed factorials; split plot; analysis of variance in regression models; optimum design. Use of existing statistical programs. Typically offered Fall and Spring. 3.0 credit hours.

**STAT 51500 -** Statistical Consulting Problem

A written report of a consultation problem involving a designed experiment or sampling plan in which the student participates with members of the Department of Statistics staff. Permission of instructor required. Typically offered Fall, Spring, and Summer. 1.0 to 3.0 credit hours.

**STAT 51600** - Basic Probability and Applications

A first course in probability, intended to serve as a background for statistics and other applications. Sample spaces and axioms of probability, discrete and continuous random variables, conditional probability and Bayes' theorem, joint and conditional probability distributions, expectations, moments and moment generating functions, law of large numbers, and central limit theorem. (The probability material in course one of the Society of Actuaries and the Casualty Actuarial Society is covered by this course.) Typically offered Fall and Spring. 3.0 credit hours.

**STAT 51700** - Statistical Inference

A basic course in statistical theory covering standard statistical methods and their application. Estimation including unbiased, maximum likelihood and moment estimation; testing hypotheses for standard distributions and contingency tables; confidence intervals and regions; introduction to nonparametric tests and linear regression. Typically offered Fall and Spring. 3.0 credit hours.

**STAT 51900** - Introduction to Probability

(MA 51900) Algebra of sets, sample spaces, combinatorial problems, independence, random variables, distribution functions, moment generating functions, special continuous and discrete distributions, distribution of a function of a random variable, limit theorems. Typically offered Fall and Spring. 3.0 credit hours.

**STAT 52000** - Time Series and Applications

A first course in stationary time series with applications in engineering, economics, and physical sciences. Stationarity, autocovariance function and spectrum; integral representation of a stationary time series and interpretation; linear filtering, transfer functions; estimation of spectrum; multivariate time series. Use of computer programs for covariance and spectral estimation. Typically offered Spring. 3.0 credit hours.

**STAT 52200** - Sampling and Survey Techniques

Survey designs; simple random, stratified, and systematic samples; systems of sampling; methods of estimation; costs. Offered in alternate years. Typically offered Spring. 3.0 credit hours.

**STAT 52400** - Applied Multivariate Analysis

Extension of univariate tests in normal populations to the multivariate case, equality of covariance matrices, multivariate analysis of variance, discriminant analysis and misclassification errors, canonical correlation, principal components, factor analysis. Strong emphasis will be placed on use of existing computer programs. Typically offered Fall. 3.0 credit hours.

**STAT 52500 - ** Intermediate Statistical Methodology

Statistical methods for analyzing data based on general/generalized linear models, including linear regression, analysis of variance (ANOVA), analysis of covariance (ANCOVA), random and mixed effects models, and logistic/loglinear regression models. Application of these methods to real world problems using SAS statistical software. Typically offered Fall and Spring. 3.0 credit hours.

**STAT 52600** - Advanced Statistical Methodology

As a sequel to STAT 52500, this course introduces some statistical modeling tools that are developed for situations where least squares regression and standard ANOVA techniques may not naturally apply. One coverage centers around two lines of models that are closely related, the generalized linear models (GLM) for regression (and ANOVA) with non Gaussian responses, and survival models for the analysis of lifetime data. Among issues to be discussed are the estimation of the models, the testing of hypotheses, and the checking of model adequacy. Data examples will be used throughout the course to illustrate the methodologies and the related software tools in R. Typically offered Fall and Spring. 3.0 credit hours.

**STAT 52700** - Introduction to Computing for Statistics

This course provides a thorough introduction to the R programming language, and its use for statistical computing and data science. The course will first look at the fundamentals of R, including different data-structures, control-flow, and the basic vocabulary. An emphasis will be placed on learning idiomatic and efficient R, covering ideas such as recycling, vectorization and functional programming. The course will then look at principles and tools for tasks like organizing data ('tidy data'), manipulating data ('data carpentry'), querying data (through topics like regular expressions) as well as visualizing data (including interactive visualizations). The material and the homework will encourage development of modular reusable code and reproducible research through ideas such as object-oriented programming and dynamic documents in R Markdown. The last part of the course will study statistical procedures such as least-squares regression, LASSO, Monte Carlo sampling and Markov chain Monte Carlo. Besides exams and homework, the course will involve a final project that students can collaborate together on. Typically offered Spring. 3.0 credit hours

**STAT 52800** - Introduction to Mathematical Statistics

Distribution of mean and s^{2} in normal samples, sampling distributions derived from the normal distribution, Chi square, t and F. Distribution of statistics based on ordered samples. Asymptotic sampling distributions. Introduction to multivariate normal distribution and linear models. Sufficient statistics, maximum likelihood, least squares, linear estimation, other methods of point estimation, and discussion of their properties, Cramer-Rao inequality and Rao-Blackwell theorem. Tests of statistical hypotheses, simple and composite hypotheses, likelihood ratio tests, power of tests. Typically offered Fall and Spring. 3.0 credit hours.

**STAT 52900** - Applied Decision Theory and Bayesian Statistics

Bayesian and decision theoretic formulation of problems; construction of utility functions and quantifications of prior information; methods of Bayesian decision and inference, with applications; empirical Bayes; combination of evidence; Bayesian design and sequential analysis; comparisons of statistical paradigms. Typically offered Summer. 3.0 credit hours.

**STAT 53200** - Elements of Stochastic Processes

(MA 53200) A basic course in stochastic models, including discrete and continuous time Markov chains and Brownian motion, as well as an introduction to topics such as Gaussian processes, queues, epidemic models, branching processes, renewal processes, replacement, and reliability problems. Typically offered Fall and Spring. 3.0 credit hours.

**STAT 53800** - Probability Theory I

(MA 53800) Mathematically rigorous, measure-theoretic introduction to probability spaces, random variables, expectation, independence, weak and strong laws of large numbers, conditional expectations, and martingales. Typically offered Spring. 3.0 credit hours.

**STAT 53900** - Probability Theory II

(MA 53900) Convergence of probability laws; characteristic functions; convergence to the normal law; infinitely divisible and stable laws; Brownian motion and the invariance principle. Typically offered Fall. 3.0 credit hours.

**STAT 54000 - **Computational Finance I

An introduction to the mathematical tools and techniques of modern finance theory, in the context of Black-Scholes option pricing. Brownian motion and its stochastic calculus, Ito's formula, and Feynman-Kac formula. Pricing and hedging of claims on Black-Scholes assets. Incomplete markets. Path-dependent options. Stochastic portfolio optimization. Typically offered Spring. 3.0 credit hours.

**STAT 54100** - Advanced Probability and Options with Numerical Methods

Stochastic interest rate models. American options from the probabilistic and PDE points of view. Numerical methods for European and American options, including binomial, trinomial, and Monte-Carlo methods. Typically offered Fall. 3.0 credit hours.

**STAT 54500** - Introduction to Computational Statistics

This introductory course covers the fundamentals of computing for statistics and data analysis. It starts with a brief overview of programming using a general purpose compiled language (C) and a statistics-oriented interpreted language (R). The course proceeds to cover data structures and algorithms that are directly relevant to statistics and data analysis and concludes with a computing-oriented introduction to selected statistical methods. A significant part of the course involves programming and hands-on experimentation demonstrating the covered techniques, ration, and Markov chain Monte Carlo methods. Typically offered Fall. 3.0 credit hours.

**STAT 54600** - Computational Statistics

The course focuses on two fundamental aspects in computational statistics: (1) what to compute and (2) how to compute. The first is covered with a brief review of advanced topics in statistical inference, including Fisher's fiducial inference, Bayesian and frequenstist methods, and the Dempster-Shafer (DS) Theory. The second is discussed in detail by examining exact, approximation, and interactive simulation methods for statistical inference with a variety of commonly used statistical models. The emphasis is on the EM-type and quasi-Newton algorithms, numerical differentiation and integration, and Markov chain Monte Carlo methods. Typically offered Spring and Summer. 3.0 credit hours.

**STAT 54900 - ** An Introduction to QTL Mapping in Experimental Populations

**STAT 55300** - Theory of Linear Models and Analysis of Experimental Designs

Least squares analysis of linear models. Gauss Markov Theorem. Estimability and testability of parameters. Confidence regions and prediction regions. Introduction to design of experiments. Analysis of variance. Factorial and block designs. Analysis of random, fixed, and mixed models. Components of variance. Distribution of linear and quadratic forms in normal vectors. A firm background in matrix algebra and some previous exposure to linear models or analysis of variance is desirable. Typically offered Spring. 3.0 credit hours.

**STAT 58200** - Statistical Consulting and Collaboration

This course is designed to emphasize and develop the skills needed by a statistical consultant/collaborator. Topics include: problem solving, consulting session management, written and oral communication, research ethics, design of experiments, collection of data, and application of statistical methods to real problems. Class activities include actively participating in consulting sessions held by the Statistical Consulting Service, small group projects, short papers, and oral presentations. Permission of Instructor required. Typically offered Spring. 3.0 credit hours.

**STAT 63800** - Stochastic Processes I

(MA 63800) Advanced topics in probability theory which may include stationary processes, independent increment processes, Gaussian processes; martingales, Markov processes, ergodic theory. Prerequisite: STAT 53900. Typically offered Fall Spring. 3.0 credit hours.

**STAT 63900** - Stochastic Processes II

(MA 63900) Continuation of STAT 63800. Typically offered Fall. 3.0 credit hours.

## Non-lecture courses

### Internships

**STAT 59000** - Internship Seminar

Students complete an internship where they will use statistical methods. A detailed report describing the internship work is required. Permission of department required. Permission of instructor required. Typically offered Fall, Spring and Summer. 1.0 to 3.0 credit hours.

### Seminars

**STAT 58100** - Bioinformatics Seminar

This is a weekly forum for presenting both applied and theoretical work in the broad area of bioinformatics. Bioinformatics is the science of generating, organizing, and analyzing biological data. This seminar series occurs both in the fall and spring semesters and attracts speakers from Purdue University, as well as throughout the world. Students are encouraged to register for this course, and everyone else is encouraged to attend this open seminar. Typically offered Fall and Spring. 1.0 credit hours.

**STAT 597** Statistical Consulting Seminar (Banner Course Number: 59700)

**Semester: **Fall Spring Summer

**Prerequisites: ** STAT 514, STAT 525, and consent of instructor

**Credits: **1

**Primary Audience: **Graduate students in Statistics

**Description: **Active participation in weekly consulting meetings, directed reading in the statistical literature, application of statistical methods to real problems, report writing. This course may be taken several times for credit, but at most, three credits may count toward fulfilling the requirements for any degree.

**STAT 598** Topics in Statistical Methods (Banner Course Number: 59800)

**Semester: **Fall Spring Summer

**Prerequisites: **

**Credits: **1-6

**Primary Audience: **

**Description: **Directed study and reports for students who wish to undertake individual reading and study on approved topics. (May be repeated for credit).

**STAT 598B** Bioinformatics/Statistical Genomics Seminar (Banner Course Number: 59800)

**Semester: **Fall Spring

**Prerequisites: **

**Credits: **1

**Primary Audience: **

**Description: **Meets the same time and place as the Bioinformatics/Statistical Genomics Seminar.

**STAT 598V** Exploring Statistical Sciences Research (Banner Course Number: 59800)

**Semester: **Fall

**Prerequisites: **

**Credits: **1

**Primary Audience: **

**Description: **Meets at same time and place as Exploring Statistical Sciences Seminar.

**STAT 691** Seminar in Probability Theory (Banner Course Number: 69100)

**Semester: **Fall Spring Summer

**Prerequisites: **Designator Required Course: Students must contact the departmental office to obtain a two digit instructor designator code.

**Credits: **1-3

**Primary Audience: **

**Description: **Individual Study

**STAT 691S** Probability Seminar (Banner Course Number: 69100)

**Semester: **Fall Spring

**Prerequisites: **It is recommended that the student has taken a graduate course in probability MA/STAT 538 and MA/STAT 539.

**Credits: **1

**Primary Audience: **

**Description: **The Probability Seminar is a weekly seminar on recent advances in the field of probability theory. Speakers from within Purdue as well as visitors from other institutions will present their recent work. Topics covered often include Markov processes, random walks, Malliavin calculus, stochastic (partial) differential equations, martingales, as well as other topics in probability theory.

**STAT 692** Statistics General Colloquium (Banner Course Number: 69200)

**Semester: **Fall Spring

**Prerequisites: **

**Credits: **1

**Primary Audience: **

**Description: **Meets at same time and place as Research Colloquia. Previously listed as 690S.

#### Dissertation research courses

**STAT 698** Research MS Thesis (Banner Course Number: 69800)

**Semester: **Fall Spring Summer

**Prerequisites: **

**Credits: **1-18

**Primary Audience: **

**Description: **

**STAT 699** Research PhD Thesis (Banner Course Number: 69900)

**Semester: **Fall Spring Summer

**Prerequisites: **

**Credits: **1-18

**Primary Audience: **

**Description: **

**STAT 699A** Research PhD Thesis Absentia (Banner Course Number: 69900)

**Semester: **Fall Spring Summer

**Prerequisites: **

**Credits: **3-18

**Primary Audience: **

**Description: **

**STAT 699B** Research PhD Thesis Absentia (Banner Course Number: 69900)

**Semester: **Fall Spring Summer

**Prerequisites: **

**Credits: **3-18

**Primary Audience: **

**Description: **

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