Statistics

STAT W1000x and y Undergraduate Seminar in Statistics 1 pt. Prerequisites: Previous or concurrent enrollment in a course in Statistics Prepared with undergraduates majoring in quantitative disciplines in mind, the presentations in this colloquium focus on the interface between data analysis, computation, and theory in interdisciplinary research. Meetings are open to all undergraduates, whether registered for the courses or not. Presenters are dawn from the faculty of department in Arts and Sciences, Engineering, Public Health and Medicine.

STAT W1001x and y Introduction to Statistical Reasoning 3 pts. Prerequisites: Some high school algebra. A friendly introduction to statistical concepts and reasoning with emphasis on developing statistical intuition rather than on mathematical rigor. Topics include design of experiments, descriptive statistics, correlation and regression, probability, chance variability, sampling, chance models, and tests of significance.

STAT W1111x and y Introduction to Statistics (without calculus) 3 pts. Prerequisites: Intermediate high school algebra. Designed for students in fields that emphasize quantitative methods. Graphical and numerical summaries, probability, theory of sampling distributions, linear regression, confidence intervals and hypothesis testing. Quantitative reasoning and data analysis. Practical experience with statistical software. Illustrations are taken from a variety of fields. Data-collection/analysis project with emphasis on study designs is part of the coursework requirement.

STAT W1211x and y Introduction to Statistics (with calculus) 3 pts. Prerequisites: one semester of calculus. Designed for students who desire a strong grounding in statistical concepts with a greater degree of mathematical rigor than in STAT W1111. Random variables, probability distributions, pdf, cdf, mean, variance, correlation, conditional distribution, conditional mean and conditional variance, law of iterated expectations, normal, chi-square, F and t distributions, law of large numbers, central limit theorem, parameter estimation, unbiasedness, consistency, efficiency, hypothesis testing, p-value, confidence intervals, maximum likelihood estimation. Serves as the pre-requisite for ECON W3412.

STAT W2024x Applied Linear Regression Analysis 3 pts. Prerequisites: One of STAT W1001, W1111, or W1211. Develops critical thinking and data analysis skills for regression analysis in science and policy settings. Simple and multiple linear regression, non-linear and logistic models, random-effects models, penalized regression methods. Implementation in a statistical package. Optional computer-lab sessions. Emphasis on real-world examples and on planning, proposing, implementing, and reporting.

STAT W2025y Applied Statistical Methods 3 pts. Prerequisites: STAT W2024 Classical nonparametric methods, permutation tests; contingency tables, generalized linear models, missing data, causal inference, multiple comparisons. Implementation in statistical software. Emphasis on on conducting data analyses and reporting the results. Optional weekly computer-lab sessions.

STAT W2026x Statistical Applications and Case Studies 3 pts. Prerequisites: STAT W2025 A sample of topics and application areas in applied statistics. Topic areas may include: Markov processes and Queuing theory; Meta-Analysis of clinical trial research; Receiver-Operator Curves in Medical Diagnosis; Spatial statistics with applications in geology, astronomy, and epidemiology; Multiple comparisons in bio-informatics; Causal modeling with missing data; statistical methods in genetic epidemiology; Stochastic analysis of neural spike train data; Graphical models for computer and social network data.

STAT W3026x Applied Data Mining 3 pts. Data Mining is a dynamic and fast growing field at the interface of Statistics and Computer Science. The emergence of massive datasets containing millions or even billions of observations provides the primary impetus for the field. Such datasets arise, for instance, in large-scale retailing, telecommunications, astronomy, computational and statistical challenges. This course will provide an overview of current practice in data mining. Specific topics covered with include databases and data warehousing, exploratory data analysis and visualization, descriptive modeling, predictive modeling, pattern and rule discovery, text mining, Bayesian data mining, and causal inference. The use of statistical software will be emphasized.

STAT W3051x or y (Section 001) Math Finance in Continuous Time 3 pts. Prerequisites: V3050 This follows Math V3050. Basic concepts in probability theory, and then advanced concepts, including Brownian motion, stochastic calculus, expectation, Radon-Nikodym theorem, Girsanov's theorem, stochastic differential equations (inlcuding Black-Merton-Scholes), options and hedging, stochastic interest rates, forwards and futures. Formal proofs will be eschewed in favor of understanding concepts.

STAT W3103x Mathematical Methods for Statistics 6 pts. Prerequisites: MATH V1101 or permission of the instructor. A fast-paced coverage of those aspects of the differential and integral calculus of one and several variables and of the linear algebra required for the core courses in the Statistics major. The mathematical topics are integrated with an introduction to computing. Students seeking more comprehensive background should replace this course with MATH V1102 and V2010 and any COMS course numbered from W1003 to W1009.

STAT W3105x Introduction to Probability 3 pts. Prerequisites: MATH V1101 and V1102 or the equivalent A calculus-based introduction to probability theory. A quick review of multivariate calculus is provided. Topics covered include random variables, conditional probability, expectation, independence, Bayes' rule, important distributions, joint distributions, moment generating functions, central limit theorem, laws of large numbers and Markov's inequality.

STAT W3107y Introduction to Statistical Inference 3 pts. Prerequisites: STAT W3105 or W4105, or the equivalent. Calculus-based introduction to the theory of statistics. Useful distributions, law of large numbers and central limit theorem, point estimation, hypothesis testing, confidence intervals maximum likelihood, likelihood ratio tests, nonparametric procedures, theory of least squares and analysis of variance.

STAT W3315x Linear Regression Models 3 pts. Prerequisites: STAT W3107 (or STAT W4150) and STAT W3103 (or MATH V1101, V1102, and V2110). Theory and practice of regression analysis. Simple and multiple regression, testing, estimation, prediction, and confidence procedures, modeling, regression diagnostics and plots, polynomial regression, colinearity and confounding, model selection, geometry of least squares. Extensive use of the computer to analyse data. Equivalent to STAT W4315 except that enrollment is limited to undergraduate students.

STAT W3997x and y Independent Research Prerequisites: The permission of a member of the department. May be repeated for credit. This course provides a mechanism for students who undertake research with a faculty member from the Department of Statistics to receive academic credit; students should only register for this course with permission of their project mentor.

SIEO W4150x and y Introduction to Probability and Statistics 3 pts. Prerequisites: MATH V1101 and V1102 or the equivalent. A quick calculus-based tour of the fundamentals of probability theory and statistical inference. Probability models, random variables, useful distributions, expectations, law of large numbers, central limit theorem, point and confidence interval estimation, hypothesis tests, linear regression. Students seeking a more thorough introduction to probability and statistics should consider STAT W3105 and W3107.

STAT W4201x and y Advanced Data Analysis 3 pts. Prerequisites: STAT W4315. At least one of W4290, W4325, W4330, W4437, W4413, W4543 is recommended. This is a course on getting the most out of data. The emphasis will be on hands-on experience, involving case studies with real data and using common statistical packages. The course covers, at a very high level, exploratory data analysis, model formulation, goodness of fit testing, and other standard and non-standard statistical procedures, including linear regression, analysis of variance, nonlinear regression, generalized linear models, survival analysis, time series analysis, and modern regression methods. Students will be expected to propose a data set of their choice for use as case study material.

STAT W4240x Data Mining 3 pts. Prerequisites: COMS W1003, W1004, W1005, W1007, or the equivalent. Corequisites: Either STAT W3105 or W4105, and either STAT W3107 or W4107. Data Mining is a dynamic and fast growing field at the interface of Statistics and Computer Science. The emergence of massive datasets containing millions or even billions of observations provides the primary impetus for the field. Such datasets arise, for instance, in large-scale retailing, telecommunications, astronomy, computational and statistical challenges. This course will provide an overview of current research in data mining and will be suitable for graduate students from many disciplines. Specific topics covered with include databases and data warehousing, exploratory data analysis and visualization, descriptive modeling, predictive modeling, pattern and rule discovery, text mining, Bayesian data mining, and causal inference.

STAT W4242 Introduction to Data Science 3 pts. Data Science is a dynamic and fast growing field at the interface of Statistics and Computer Science. The emergence of massive datasets containing millions or even billions of observations provides the primary impetus for the field. Such datasets arise, for instance, in large-scale retailing, telecommunicatios, astronomy, and internet social media. This course will emphasize practical techniques for working with large-scale date. Specific topics covered will include statistical modeling and machine learning, data pipelines, programming languages, "big data" tools, and real world topics and case studies. The use of statistical and data manipulation software will be required.

STAT W4249y Applied Data Science 3 pts. Data scientists wear many caps. This course presents two from opposite ends of the spectrum. Coding best practices will be taught using test-driven development, version control, and colloboration. The Python programming wil be used. Students finish the class with a portfolio on GitHub, and an understanding of several core statistical/machine-learning algorithms. Case studies give students the opportunity to use this sotware with real world data sets. Here they develop intuition for extracting meaning from data. Students finish the class with a wordpress portfolio.

STAT W4290y Statistical Methods in Finance 3 pts. Prerequisites: STAT W3107 or W4107. A fast-paced introduction to statistical methods used in quantitative finance. Financial applications and statistical methodologies are intertwined in all lectures. Topics include regression analysis and applications to the Capital Asset Pricing Model and multifactor pricing models, principal components and multivariate analysis, smoothing techniques and estimation of yield curves statistical methods for financial time series, value at risk, term structure models and fixed income research, and estimation and modeling of volatilities. Hands-on experience with financial data.

STAT W4325y Generalized Linear Models 3 pts. Prerequisites: STAT W4315 Statistical methods for rates and proportions, ordered and nominal categorical responses, contingency tables, odds-ratios, exact inference, logistic regression, Poisson regression, generalized linear models.

STAT W4330x Multilevel Models Prerequisites: STAT W4315 Theory and practice, including model-checking, for random and mixed-effects models (also called hierarchical, multi-level models). Extensive use of the computer to analyse data.

STAT W4335x Sample Surveys 3 pts. Prerequisites: STAT W3107 or W4107. Introductory course on the design and analysis of sample surveys. How sample surveys are conducted, why the designs are used, how to analyze survey results, and how to derive from first principles the standard results and their generalizations. Examples from public health, social work, opinion polling, and other topics of interest.

STAT W4400y Statistical Machine Learning Prerequisites: Calculus I and Linear Algebra The course will provide an introduction to Machine Learning and its core models and algorithms. The aim of the course is to provide students of statistics with detailed knowledge of how Machine Learning methods work and how statistical models can be brought to bear in computer systems - not only to analyze large data sets, but to let computers perform tasks that traditional methods of computer science are unable to address. Examples range from speech recognition and text analysis through bioinformatics and medical diagnosis. This course provides a first introduction to the statistical methods and mathematical concepts which make such technologies possible.

STAT W4413y Nonparametric Statistics 3 pts. Prerequisites: STAT W3107 or W4107. Statistical inference without parametric model assumption. Hypothesis testing using ranks, permutations, and order statistics. Nonparametric analogs of analysis of variance. Non-parametric regression, smoothing and model selection.

STAT W4437x and y Time Series Analysis 3 pts. Prerequisites: STAT W4315 or the equivalent. Least squares smoothing and prediction, linear systems, Fourier analysis, and spectral estimation. Impulse response and transfer function. Fourier series, the fast Fourier transform, autocorrelation function, and spectral density. Univariate Box-Jenkins modeling and forecasting. Emphasis on applications. Examples from the physical sciences, social sciences, and business. Computing is an integral part of the course.

STAT W4440x Linear Regression and Time Series Methods 3 pts. Prerequisites: STAT W4107 or permission of program advisor. A one semester course covering: Simple and multiple regression, including testing, estimation, and confidence procedures, modeling, regression diagnostics and plots, polynomial regression, colinearity and confounding, model selection, geometry of least squares. Linear time series models. Auto-regressive, moving average and ARIMA models. Estimation and forecasting with time series models. Confidence intervals and prediction error. Students may not receive credit for more than two of STAT W4315, W4437, and W4440. Satisfies the SOA VEE requirements in regression and in time-series.

STAT W4543y Survival Analysis Prerequisites: STAT W4315. Survival distributions, types of censored data, estimation for various survival models, nonparametric estimation of survival distributions, the proportional hazard and accelerated lifetime models for regression analysis with failure-time data. Extensive use of the computer.

STAT W4606x and y Elementary Stochastic Processes 3 pts. Prerequisites: STAT W3105, W4105, or the equivalent. Review of elements of probability theory. Poisson processes. Renewal theory. Wald's equation. Introduction to discrete and continuous time Markov chains. Applications to queueing theory, inventory models, branching processes.

STAT W4635y Stochastic Processes for Finance 3 pts. Prerequisites: STAT W3105, W4105, or equivalent. This course covers theory of stochastic processes applied to finance. It covers concepts of Martingales, Markov chain models, Brownian motion. Stochastic Integration, Ito's formula as a theoretical foundation of processes used in financial modeling. It also introduces basic discrete and continuous time models of asset price evolutions in the context of the following problems in finance: portfolio optimization, option pricing, spot rate interest modeling.

ACTU K4821x and y Actuarial Methods 3 pts. Prerequisites: STAT W4105, STAT W4840 This course covers the non-stochastic process portions of the MLC/3L exam, and is about pricing and reserving of life insurance. Topics include actuarial present value, the equivalence principle, premiums, three methods of calculating reserves, joint life and multiple hazard.

ACTU K4823x and y Actuarial Models 3 pts. Prerequisites: STAT W4840, STAT W4107 This course covers portions of the C/4 exam not covered elsewhere in the curriculum. Topics may include Bayesian statistics, credibility, and risk measures.

STAC K4830x Stochastic Processes for Actuarial Science 3 pts. Prerequisites: STAT W4606 This course covers the material and the theoretical background for exam MFE. Subjects include discrete time option pricing, martingales, change of measure/Girsanov's Theorem, Brownian motion, diffusions, interest rate models, and stochastic integration.

STAT W4840x Theory of Interest 3 pts. Prerequisites: MATH V1101 or the equivalent. Introduction to the mathematical theory of interest as well as the elements of economic and financial theory of interest. Topics include rates of interest and discount; simple, compound, real, nominal, effective, dollar (time)-weighted; present, current, future value; discount function; annuities; stocks and other instruments; definitions of key terms of modern financial analysis; yield curves; spot (forward) rates; duration; immunization; and short sales. The course will cover determining equivalent measures of interest; discounting; accumulating; determining yield rates; and amortization.