杏吧论坛

Dr Yining Chen

This course is available on the MSc in Data Science, MSc in Operations Research & Analytics, MSc in Statistics, MSc in Statistics (Financial Statistics), MSc in Statistics (Financial Statistics) (杏吧论坛 and Fudan), MSc in Statistics (Financial Statistics) (Research), MSc in Statistics (Research), MSc in Statistics (Social Statistics) and MSc in Statistics (Social Statistics) (Research). This course is available with permission as an outside option to students on other programmes where regulations permit.

An introduction to the use of numerical linear algebra, optimisation, numerical integration and simulation in statistical computation, with their applications in statistical methods, including least squares, maximum likelihood, principle component analysis, LASSO, etc. If time permits, more advanced topics such as kernel methods and graphical LASSO will also be covered. Throughout the course, students will gain practical experience of implementing these computational methods in a programming language. Learning support will be provided for at least one programming language, such as R, Python or C++, but the choice of language supported may vary between years, depending on judged benefits to students, whether in terms of pedagogy or resulting skills. This year, the default choice is Python.

20 hours of lectures and 10 hours of computer workshops in the MT.

Lectures will cover:

(1) Introduction to Tools in Numerical Analysis: linear algebra (Gaussian elimination, Cholesky decomposition, matrix inversion and condition); numerical optimization (bi-section, steepest descent, Newton’s method, Quasi-Newton methods, stochastic search); convex optimization (coordinate descent, ADMM); numerical integration.

(2) Introduction to Tools in Numerical Simulation: random number generation (inverse CDF, rejection, Box-Muller, etc); Introduction to Monte-Carlo methods.

(3) Applications in Statistics: linear regression and least squares; generalised linear models; principle component analysis (PCA); Page rank;  LASSO.

(4) Other advanced topics if time allows: bootstrapping; kernel density estimation; Graphical models and Graphical LASSO.

Students will be expected to produce 4 problem sets in the MT.

Bi-weekly exercises, involving computer programming and some theory.

Computational Statistics by Givens and Hoeting

Statistical computing in C++ and R by Eubank and Kupresanin

The Art of R Programming: A Tour of Statistical Software Design by Matloff

Think Python: How to Think Like a Computer Scientist by Downey

Exam (70%, duration: 2 hours) in the summer exam period.
Coursework (30%) in the MT.