Bootstrap and Resampling Methods

 
Semester 2 2021
Sunday 17-20, http://www.tau.ac.il/ ∼ saharon/Resampling.html
Lecturer: Saharon Rosset
Schreiber 022
saharon@tauex.tau.ac.il
Office hrs: By appointment.

Announcements and handouts

(7 March)
Intro to Bootstrap presentation
(14 March)
Homework 1 due on 4 April during the break (note there will be a second homework due shortly after the break)
(24 March)
Exponential simulation code
(28 March)
Homework 2 due on 18 April before class (the second class after the break). All problems except the last one can be solved with material we already covered.
(18 April)
R code for stamps example
(2 May)
Presentation on Efron et al.'s analysis of bootstrap for phylogenetic tree inference (originally prepared by Aya Vituri)
(4 May)
Homework 3 due on 23 May before class.
(9 May)
Breiman's paper Heuristics of instability and stabilization in model selection
Code example for running the Metropolis algorithm on circles in a rectangle
Class 9 recording
(23 May)
Assaf's presentation
Class 10 recording
(30 May)
Homework 4 due on 13 June. For the extra credit part of Problem 1 use Assaf's python code (Corrected on 7 June)
R code for running Gibbs sampling on the Beta-Binomial example
Class 11 recording
(6 June)
Class 12 recording
R code for using MCMC for importance sampling of permutations to calculate tail probabilities
(13 June)
Class 13 recording
Some HW solutions: HW2, HW3

Syllabus

The goal of this course is to introduce the main ideas and uses of the Bootstrap and related methods.
The first part of the course will follow the book Än Introduction to the Bootstrap" by Efron and Tibshirani.
We will cover chapters 1-19 and possibly some material from later chapters.
The rest of the course will cover some of the following areas, as time and the mutual interest of instructor and students dictate:  
Preliminary plan:
Week 1: Introduction, up to chapter 6
Week 2: Chap. 7-10
Week 3: Chap. 11-12
Week 4-7: Chap. 13-20
Week 8-9: Bootstrap applications from the literature
Week 10-12: Markov Chain Monte Carlo (MCMC) introduction and applications, importance sampling
The final grade will be based on a combination of homework and a final take home exam. The homework and exam will require a combination of theoretical work and some programming and data analysis.

Prerequisites

Solid knowledge of mathematical foundations: Calculus; Linear Algebra
Undergraduate courses in: Probability; Statistical Theory; Applied Statistics (e.g., Regression)
Statistical programming experience in R is an advantage

Main textbook

An Introduction to the Bootstrap by Efron and Tibshrani (1993, Chapman and Hall). The library has several hard copies, but we now have online access to the electronic copy for all TAU users.

Other resources

Papers on bootstrap we discussed:
Confidence limits on phylogenies: an approach using the bootstrap by Felsenstein
Bootstrap confidence levels for phylogenetic trees by Efron et al. 1996
Heuristics of instability and stabilization in model selection by Breiman
Resources on MCMC and related topics:
The Monte-Carlo Method by Paul J. Atzberger
An Introduction to MCMC for Machine Learning by Andrieu et al.

Computing

The course will require some use of statistical modeling software. It is strongly recommended to use R (freely available for PC/Unix/Mac).
R Project website also contains extensive documentation.
A basic "getting you started in R" tutorial. Uses the Boston Housing Data (thanks to Giles Hooker).
Modern Applied Statistics with Splus by Venables and Ripley is an excellent source for statistical computing help for R/Splus.



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On 14 Jun 2021, 18:35.