Semester 2 2021

Sunday 17-20, http://www.tau.ac.il/ ∼ saharon/Resampling.html

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. |

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

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:

- 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:

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.

Undergraduate courses in: Probability; Statistical Theory; Applied Statistics (e.g., Regression)

Statistical programming experience in R is an advantage

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.

R Project website also contains extensive documentation.

A basic "getting you started in R" tutorial. Uses the Boston Housing Data (thanks to Giles Hooker).

File translated from T

On 14 Jun 2021, 18:35.