Statistics

Prerequisites: some high school algebra. Designed for students in fields that emphasize quantitative methods. This course satisfies the statistics requirements of all majors except statistics, economics, and engineering. Graphical and numerical summaries, probability, theory of sampling distributions, linear regression, confidence intervals, and hypothesis testing are taught as aids to quantitative reasoning and data analysis. Use of statistical software required. Illustrations are taken from a variety of fields. Data-collection/analysis project with emphasis on study designs is part of the coursework requirement.

Prerequisites: some high school algebra. Designed for students in fields that emphasize quantitative methods. This course satisfies the statistics requirements of all majors except statistics, economics, and engineering. Graphical and numerical summaries, probability, theory of sampling distributions, linear regression, confidence intervals, and hypothesis testing are taught as aids to quantitative reasoning and data analysis. Use of statistical software required. Illustrations are taken from a variety of fields. Data-collection/analysis project with emphasis on study designs is part of the coursework requirement.

Prerequisites: working knowledge of calculus (differentiation and integration). 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. Satisfies the pre-requisites for ECON W3412.

Prerequisites: working knowledge of calculus (differentiation and integration). 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. Satisfies the pre-requisites for ECON W3412.

Prerequisites: A good working knowledge of calculus, including derivatives, single and double, limits, sums and series. Life is a gamble and with some knowledge of probability / statistics is easier evaluate the risks and rewards involved. Probability theory allows us take a known underlying model and estimate how likely will we be able to see future events. Statistical Inference allows us to take data we have seen and estimate the missing parts of an unknown model. The first part of the course focus on the former and the second part the latter.

Prerequisites: MATH V1101 Calculus I and MATH V1102 Calculus II, or the equivalent, and STAT W1111 or STAT W1211 (Introduction to Statistics). Corequisites: MATH V1201 Calculus III, or the equivalent, or the instructor's permission. This course can be taken as a single course for students requiring knowledge of probability or as a foundation for more advanced courses. It is open to both undergraduate and master students. This course satisfies the prerequisite for STAT W3107 and W4107. Topics covered include combinatorics, conditional probability, random variables and common distributions, expectation, independence, Bayes' rule, joint distributions, conditional expectations, moment generating functions, central limit theorem, laws of large numbers, characteristic functions.

Prerequisites: STAT W3105 Intro. to Probability or STAT W4105 Probability, 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.

Prerequisites: STAT GU4204 or the equivalent, and a course in linear algebra. 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.

Prerequisites: STAT GU4204 and GU4205 or the equivalent. Introduction to programming in the R statistical package: functions, objects, data structures, flow control, input and output, debugging, logical design, and abstraction. Writing code for numerical and graphical statistical analyses. Writing maintainable code and testing, stochastic simulations, paralleizing data analyses, and working with large data sets. Examples from data science will be used for demonstration.

Prerequisites: STAT GU4205 or the equivalent. Prerequisites: STAT GU4205 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.

This course introduces the Bayesian paradigm for statistical inference.  Topics covered include prior and posterior distributions: conjugate priors, informative and non-informative priors; one- and two-sample problems; models for normal data, models for binary data, Bayesian linear models; Bayesian computation: MCMC algorithms, the Gibbs sampler; hierarchical models; hypothesis testing, Bayes factors, model selection; use of statistical software.

Prerequisites: A course in the theory of statistical inference, such as STAT GU4204 a course in statistical modeling and data analysis, such as STAT GU4205.

 

Prerequisites: STAT GU4206 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.

Prerequisites: STAT GU4204 and STAT GU4205 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.

Prerequisites: At least one semester of calculus. A calculus-based introduction to probability theory. 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 Markovs inequality.

Prerequisites: STAT GR5203 or the equivalent, and two semesters of calculus. 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.

Prerequisites: STAT GR5203 and GR5204 or the equivalent. Theory and practice of regression analysis, 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. Extensive use of the computer to analyse data.

Prerequisites: STAT GU5204 and STAT GU5205 Open to MA students in Statistics only Introduction to programming in the R statistical package: functions, objects, data structures, flow control, input and output, debugging, logical design, and abstraction. Writing code for numerical and graphical statistical analyses. Writing maintainable code and testing, stochastic simulations, paralleizing data analyses, and working with large data sets. Examples from data science will be used for demonstration.

Open to MA students in Statistics only Prerequisites: STAT GU4205 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.

This course introduces the Bayesian paradigm for statistical inference.  Topics covered include prior and posterior distributions: conjugate priors, informative and non-informative priors; one- and two-sample problems; models for normal data, models for binary data, Bayesian linear models, Bayesian computation: MCMC algorithms, the Gibbs sampler; hierarchical models; hypothesis testing, Bayes factors, model selection; use of statistical software.

 

Prerequisites: A course in the theory of statistical inference, such as STAT GU4204/GR5204 a  course in statistical modeling and data analysis such as STAT GU4205/GR5205.

Prerequisites: STAT GR5206 or the equivalent. Open to MA students in Statistics only 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.

Prerequisites: STAT GR5204 or the equivalent. STAT GR5205 is recommended. Open to MA students in Statistics only 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.