STATS 4CI3/6CI3, Winter 2019
COMPUTATIONAL METHODS FOR INFERENCE
This course will focus on computationally intensive Monte Carlo methods and their uses in statistical inference. Computing is a key concept in this course and will be conducted in the statistical programming language R. The first part of the course will be focussed on learning the syntax of R and how to write complex programs to implement mathematical and statistical algorithms. This will include learning to write functions and key concepts such as conditional statements and iteration. Monte Carlo and simulation techniques involve generation of random variables. Although computers cannot do this the course will explain how computers can generate pseudo-random numbers which behave as if they are truly random. Monte Carlo methods to approximate integrals will then be studied along with ways to improve the efficiency of such methods. Students will then be introduced to the important concept of simulation studies to evaluate statistical algorithms. The second half of the course will examine the use of Monte Carlo methods in statistical inference. The concept of Bayesian inference will be introduced with particular emphasis on Markov chain Monte Carlo methods often used to avoid complex calculations that often arise in this setting. For frequentist inference the jackknife and bootstrap methods for bias and variance calculation will be studied as will the use of the bootstrap for interval estimation. Finally bootstrap and permutation techniques for hypothesis testing will be studied.
INSTRUCTOR: A. Canty
Monte Carlo methods; bootstrap and jackknife methods; multi-parameter maximum likelihood; computation in nonlinear likelihood inference; The EM Algorithm; sufficiency and its applications; optimal hypothesis tests; Bayesian inference; Markov Chain Monte Carlo.
Three lectures; one term
Prerequisite(s): STATS 3D03
Antirequisite(s): STATS 3CI3