Probability and statistics seminar: Sampling Contingency Tables
- Date: –11:15
- Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64121
- Lecturer: Igor Pak, University of California (UCLA)
- Organiser: Matematiska institutionen
- Contact person: Gabriel Berzunza Ojeda
Abstract: Contingency tables are integer matrices with fixed row and column sums. Sampling them efficiently is a notoriously challenging problem both in both theory and practice, of great interest in both theoretical and the real world statistics. Roughly speaking, random sampling of contingency tables allows one to measure the empirical correlation between discrete random variables, always a good thing to have.
I will first give a brief overview of the existing approaches (Fisher-Yates sampling, sequential sampling, the Diaconis-Gangolli MCMC algorithm and the algebraic statistic tools). I will then describe a new MCMC sampling algorithm based on combinatorial and group theoretic ideas. Many examples will follow which will illustrate the surprising power of our algorithm both in two and higher dimensions. If time permits, I will mention the theory behind our work and some potential generalizations we are thinking about.