STAT 812/420 Computational Statistics

Description

Computationally intensive methods have become widely used in statistical inference. The objective of this course is to teach students important computational techniques used in statistical inference (evaluation of statistical methods, MLE and Bayesian inference). After learning this course, students are expected to gain understanding of algorithms behind statistical inferential methods, be able to develop new statistical methods, be able to use computer to investigate the properties of statistical methods, and be able to implement a combination of standard statistical toolkits for analyzing real data sets.

Prerequisites: multivariate calculus (MATH 225), basic algebra (MATH 164), an introductory statistics (eg. STAT 245), a probability course (eg. STAT 342), a course in regression (eg. STAT 344).

List of Topics with Associated Course Materials

Topic	Academic Week
1. Introduction to Statistical Inference and R
1.1 A very short introduction to R and Rstudio, Introduction to R by R core team 1.2 R code for introducing basic R features (Unit 1)	1
2. Computer Arithmetic
2.1 Overflow, underflow and rounding errors (Unit 2)	2
3. Basics of Monte Carlo Methods
3.1 Random numbers generator and inverting CDF sampling (Unit 3)	3
3.2 Simulation for Studying Point Estimation and Hypothesis Testing (Unit 4)	4
4. Maximum Likelihood Estimation and Optimization Methods
4.1 Univariate Optimization • Introduction to maximum likelihood estimation • Univariate Optimization (Unit 5) • A Shiny App for Finding Square Root using Newton Method	5
4.2 Multivariate Optimization Methods (Unit 6)	6
4.3 EM Algorithm • Introduction to EM algorithm • EM Algorithm (Unit 7)	7
5. Bayesian Inference and Advanced Monte Carlo Methods
5.1 Introduction to Bayesian Inference 5.2 Numerical Quadrature • Animations for Demonstrating Numerical Integration • Numerical Quadrature (Unit 8)	8
5.3 Laplace Approximation (Unit 9) 5.4 Rejection Sampling (Unit 10)	9
5.5 Importance Sampling (Unit 11)	10
5.6 Introduction to MCMC Convergence (Unit 12) 5.7 Gibbs sampling (Unit 13)	11
5.8 Metropolis-Hastings Sampling • Metropolis-Hasting Sampling (animation) • Metropolis-Hastings Sampling (Unit 14)	12
5.9 General-purpose Samplers • JAGS sampling • STAN sampling for a stochastic volatility model (Unit 16)	13

Note

The R markdown sources for producing the HTML files listed above can be found in this Github folder.