Enrolment options
The course will introduce modern methods of statistical inference which use computational methods of analysis. These methods such as permutation tests and bootstrapping are nowadays used in business, finance, and scientific research. The focus is on statistical methods that use computation to replace certain assumptions. Students will learn how to manipulate data, design and perform simple Monte Carlo experiments, and be able to use resampling methods such as the Boot-strap. Although the main focus will be put on understanding the methods, programming language R will be used to implement them.
Expected outcomes
1) Should be able to write R code, and be able to modify and understand existing R code.
2) Understand basic data structures and algorithms in statistical applications.
3) Understand basic numerical methods such as optimization, sampling, etc.
4) Learn some statistics topics such as bootstrap, linear/logistic regression.
Indicative Content
Unit 1: R Programming Introduction
Unit 2: Introduction: Distributions of random variables; Classical parametric hypothesis testing; p-values.
Unit 3: Nonparametric tests: Permutation tests; Rank tests; Matched pairs.
Unit 4: The bootstrap: The jackknife; The empirical distribution; The nonparametric bootstrap; The parametric bootstrap; Bootstrap confidence intervals; Bootstrapping linear models.
Unit 5: Cross-validation: Leave-one-out cross-validation; Cross-validation for smoothing splines; k-fold cross-validation; Cross-validation for likelihood-based models.
Reference
James E. Gentle, Elements of Computational Statistics.
Efron and Tibshirani, An Introduction to the Bootstrap.
Computational Statistics Handbook with MATLAB®.
G.H. Givens and J.A. Hoeting, “Computational Statistics”, 2nd edition, Wiley, 2012.