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# Charles MARGOSSIAN (Columbia) – “Nested $\hat R$: Assessing the convergence of Markov chains Monte Carlo when running many short chains”

July 7 @ 2:00 pm - 2:45 pm

Statistical Seminar:
Time: 2:00 pm -2.45pm
Date: 07th of July 2022
Place: Room 3001

Charles MARGOSSIAN (Columbia)  – “Nested $\hat R$: Assessing the convergence of Markov chains Monte Carlo when running many short chains”

Abstract: The growing availability of hardware accelerators, such as GPUs, has generated interest in MCMC strategies where we run many chains in parallel. After the warmup phase, precise Monte Carlo estimators can be constructed using a short sampling phase, potentially with a single iteration. To implement this approach, we need a reliable diagnostic for MCMC convergence. A natural candidate is the widely used $\hat R$ statistic, also known as the potential scale reduction factor. I demonstrate shortcomings with $\hat R$ in the many-short-chains regime and present a useful generalization, termed the Nested $\hat R$. In addition, studying convergence diagnostics gives us principled guidelines to choose the number of chains, as well as the length of the warmup and sampling phases — tuning parameters otherwise chosen using heuristics or trial-and-error.

References: A preprint is available on arxiv
(https://arxiv.org/pdf/2110.13017.pdf). This manuscript is currently being revised. A more recent version of this work can be found in my thesis (https://academiccommons.columbia.edu/doi/10.7916/0wsc-kz90, chapter 3).

Organizers:
Cristina BUTUCEA (CREST), Alexandre TSYBAKOV (CREST), Karim LOUNICI (CMAP) , Jaouad MOURTADA (CREST)