Announcements and handouts

19 March
Intro to Bootstrap presentation
Uniform example

27 March
Homework 1, due on 11 April at the beginning of the Pesach vacation.

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 ”An 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:

• Applications of Bootstrap in various scientific areas: Biology and Genetics, Economics, etc.

• Advanced theoretical topics around the bootstrap: confidence interval methodologies like BC_a and ABC; Little and tiny bootstrap; etc.

• Other randomization-based algorithms in statistics, in particular Markov Chain Monte Carlo (MCMC) and its applications.

 
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 (30% of final grade) and a final take home exam (70% of grade). 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 may discuss:
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. Class code will be in R (freely available for PC/Unix/Mac), but Python and others can also be used.
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.