Statistics

This course offers a basic study of business and economics statistics. It discusses probability theory, distribution models, sampling, and descriptive statistics. By using realistic examples from the current economic environment, students practice solving problems.  

This course examines different statistical distributions and how to apply them for hypothesis testing. Students learn to solve adjustment problems with a singular design matrix, e.g. free network adjustment. The course discusses quality assessment of adjustment results with respect to precision and reliability. Students learn to detect blunders in the observations and to evaluate the geometry of adjustment problems from partial redundancies. Students are able to solve arbitrary adjustment problems with conditions and constraints, e.g. from a rigorous solution of the nonlinear Gauss-Helmert model. They study the concept of robust parameter estimation and when to apply it. They also study how to apply the concepts of statistic and adjustment calculation for analysis of stochastic processes, e.g. time series analysis. Course topics include statistical distributions and confidence intervals, hypothesis testing, least‐squares adjustment with singular design matrix A, free net adjustment, adjustment with observed unknowns, quality assessment of adjustment results, data snooping, S‐transformation, Gauss‐Helmert model, variance component estimation, and robust parameter estimation.

This course is an introduction to the statistical learning techniques commonly used to analyze high-dimensional (or multivariate) data. It covers penalized regression, classification trees, clustering, dimension-reduction, bagging, stacking, boosting, random forests and ensemble learning.

The course covers the fundamental aspects of probability theory and the principles of statistical inference. Upon successful completion of this course, students are able to perform a rigorous data analysis: i) manipulate and summarize data; ii) visualize and understand relationships inside data; iii) apply the appropriate tools of probability theory and inferential statistics to extract useful information, test hypotheses and make predictions.

The course content is divided into 9 parts:

1. Introduction to data: Data basics; Sampling principles; Experiments and observational studies
2. Summarizing data: Examining numerical data; Considering categorical data
3. Probability: Defining probability; Conditional probability; Bayes theorem
4. Random variables: Discrete and continuous; Expectation; Linear combination; Central limit theorem
5. Distributions of random variables: Normal; Geometric; Binomial
6. Foundations for inference: Point estimates and sampling variability; Confidence intervals; Hypothesis testing
7. Inference for numerical data: One-sample means; Paired data; Difference of two means
8. Inference for one proportion
9. Introduction to linear regression: Fitting a line, residuals and correlation; Least squares regression; Diagnostics

This course explores the foundations of data science from three perspectives: inferential thinking, computational thinking, and real-world relevance. It focuses on critical concepts and skills in computer programming and statistical inference, in conjunction with hands-on analysis of real-world datasets, including economic data, document collections, geographical data, and social networks. This course also delves into social and legal issues surrounding data analysis, including issues of privacy and data ownership.

The curriculum and format are designed specifically for students who have not previously taken statistics or computer science courses. Students with some prior experience in either statistics or computing are welcome to enroll and often find that this course offers a new perspective that blends computational and inferential thinking. Students who have taken several statistics or computer science courses should instead take a more advanced course.

This course deals with the application of statistical methods to test hypotheses and draw inferences from data, using maximum likelihood methods. The course starts by developing general-purpose maximum likelihood methods, with interval estimation by means of the information matrix and the bootstrap. It goes on to develop generalized linear models, linear models and analysis of variance models as special cases of maximum likelihood methods. It covers diagnostic methods, including methods for selecting between models, checking assumptions and testing goodness-of-fit. It has an applied focus, with extensive use of R to give students practice in doing inference with real datasets, from problem formulation through to final conclusions.

Machine learning is concerned with algorithms that process relevant data and then perform some task. Often, performance of machine learning algorithms is measured statistically, and the algorithms themselves are heavily influenced by statistical ideas. For example, after observing several (x,y) pairs an algorithm may be able to predict with high accuracy the corresponding value of y for an unseen x. When the data is complex and/or high-dimensional, a number of statistical and algorithmic issues arise: a sufficiently rich class of statistical models must be used effectively and irrelevant data should be identified and then discarded. Students understand the statistical approach to analyzing data, and how it can be used to effectively perform tasks under appropriate assumptions. This enables students to formulate various real-life problems as statistical learning tasks and use common techniques to develop solutions.

This course provides a continuation of the study of medical statistics, with emphasis on more advanced topics in epidemiological methods and the design and analysis of clinical trials. Students learn how to model survival data using parametric regression models; to develop and validate a risk prediction model; to analyze clustered data using a regression model; to design and analyze a cross-over trial, cluster randomized trial, equivalence trial, and early phase trial; to understand the issues concerning interim analyses and missing data; and to carry out a meta-analysis.

This is a basic course in designing experiments and analyzing the resulting data. It is intended for engineers, physical/chemical scientists, and scientists from other fields such as biotechnology and biology. The course deals with the types of experiments that are frequently conducted in industrial settings. Its objective is to learn how to plan, design, and conduct experiments efficiently and effectively, and analyze the resulting data to obtain objective conclusions. Both design and statistical analysis issues are discussed. Opportunities to use the principles taught in the course arise in all phases of engineering and scientific work, including technology development, new product design and development, process development, and manufacturing process improvement. Applications from various fields of engineering (including chemical, mechanical, electrical, materials science, industrial, etc.) will be illustrated throughout the course. Topics include simple design with fixed and random effects. Simultaneous confidence intervals. Requirements for analysis of variance: transformations, model validation, residual analysis. Factorial design with fixed, random, and mixed effects. Additivity and interaction. Complete and incomplete designs. Randomized block designs, Latin squares and confounding. Regression and analysis of covariance. Admission requirements include FMAA20 Linear Algebra with Introduction to Computer Tools or FMAA21 Linear Algebra with Numerical Applications or FMAB20 Linear Algebra or FMAB22 Linear Algebra and FMAB30 Calculus in Several Variables or FMAB35 Calculus in Several Variables or FMSF20 Mathematical Statistics, Basic Course or FMSF25 Mathematical Statistics - Complementary Project or FMSF32 Mathematical Statistics or FMSF45 Mathematical Statistics, Basic Course or FMSF50 Mathematical Statistics, Basic Course or FMSF55 Mathematical Statistics, Basic Course or FMSF70 Mathematical Statistics or FMSF75 Mathematical Statistics, Basic Course or FMSF80 Mathematical Statistics, Basic Course. Assumed prior knowledge: Basic mathematical statistics and programming experience.

A wide range of phenomena from areas as diverse as physics, economics, and biology can be described by simple probabilistic models. Often, phenomena from different areas share a common mathematical structure. In this course a variety of mathematical structures of wide applicability is described and analyzed. The emphasis is on developing the tools which are useful to anyone modelling applications, rather than the applications themselves Students should have a good knowledge of first year probability and of basic material from first year analysis. As the course builds on Probability 1, it also deepens students' understanding of the basis of probability theory.