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# Statistics

(last modified 07.02.2017)

Contact person: Professor Victor M. Panaretos

**Bachelor (3rd and 4th semester):**

- Probabilités (MATH-230)
- Statistique (MATH-240)

**Bachelor (5th and 6th semesters):**

- Mesure et Integration (MATH-303)
- Applied Stochastic Processes (MATH-332)
- Linear Models (MATH-341)
- Time Series (MATH-342)

**Master:**

- Probability Theory (MATH-432)
- Robust and Nonparametric Statistics (MATH-441)
- Statistical Theory (MATH-442)
- Statistique Multivariée (MATH-444)
- Risk, Rare Events, and Extremes (MATH-447)

**Description :**

All students take the 2nd year courses in Probability (MATH-230) and Statistics (MATH-230). MATH-230 provides a rigorous introduction to the key notions of probability, including important limit theorems. MATH-240 gives a rigorous introduction to one-parameter i.i.d. inference (estimation, testing, confidence intervals).

The courses on Linear Models (MATH-341) and Time Series (MATH-342) are core courses for the Statistics track. They consider two important modes of departure from the standard "i.i.d" setup encountered in the second year. In MATH-341, the data remain independent but have differing parameters, subject to linear constraints, and with Gaussian behaviour. In MATH-342, the data may have the same distribution (stationary), but are typically dependent. The course on Applied Stochastic Processes (MATH-332) is also strongly recommended. It considers more general dependence structures, emphasising both dependence as well as non-stationarity, primarily through the notion of Markov chains. Students considering the potential of higher studies in Statistics are strongly encouraged to take the course on Measure and Integration (MATH-303). This provides the necessary mathematical background for the study of mathematical statistics.

The master level courses in statistics cover more advanced material, building on the third year courses. Advanced Regression (MATH-408), is the natural follow-up to the course on Linear Models (MATH-341), exploring nonlinear and non-Gaussian effects of explanatory variables. Robust and Nonparametric Statistics (MATH-441) treats the problem of carrying out statistical inference that is resistant to departures from model assumptions, or that does not formulate a parametric model at all. Statistical theory (MATH-442) treats the theoretical foundation of statistics, including optimality theory and asymptotic theory. Multivariate statistics (MATH-444) treats the problem of inference for collections of random vectors. Risk, Rare events, and Extremes (MATH-447) deals with the problem of formulating and estimating the risk associated with improbable events. The course in Probability Theory (MATH-432), takes a second look at probability, using the tools of measure theory; it is strongly recommended for students wishing to pursue further graduate study in Statistics.

Further to the courses listed above, there are three more courses that are given from time to time:

- Statistics for Genomic Data Analysis (MATH-443) explores the key challenges and statistical techniques used to analyse massive genomic data using statistical methods.
- Monte Carlo Inference (MATH-???) considers the use of modern computational capabilities to carry out simulation-based inference, including Bayesian methods.
- Biostatistics (MATH-449) presents some of the core methods and applications of statistics in the life sciences and medicine.

**Some other Math courses related to statistics:**

- All courses in the probability track are related to statistics and are particularly recommended.
- The courses on Numerical Analysis (MATH-250) and the subsequent course on Numerical integration of stochastic differential equations (MATH-452) can be particularly useful as background for nonparametric statistics, and for functional data analysis, respectively.

The course on Computational Linear Algebra (MATH-453) considers numerical methods to solve large-scale linear algebra problems, which can be particularly pertinent in multivariate and high-dimensional statistics when massive amounts of data need to be stored and manipulated for the purposes of inference.

The course on Discrete Optimization (MATH-261) is a core course taken by all students, and has important links with statistical inference problems related to discrete structures.

The course on Convexity (MATH-461) explores aspects of high dimensional geometry that are central to many methods of modern high dimensional statistics.

**Related Minors :**

Data Science (forthcoming)