Author: Pierre Jacob

This post is about estimating the parameter of a Bernoulli distribution from observations, in the “Dempster” or “Dempster–Shafer” way, which is a generalization of Bayesian inference. I’ll recall what this...continue reading.

Hi all, This post is about a way of sampling from a Categorical distribution, which appears in Arthur Dempter‘s approach to inference as a generalization of Bayesian inference (see Figure...continue reading.

Hi everyone, This short post is just to point to a course on “Couplings and Monte Carlo”, available here https://sites.google.com/site/pierrejacob/cmclectures. Versions of the course were given in Université Paris-Dauphine in...continue reading.

Hi everyone, and Happy New Year! This post is about some statistical inferences that one can do using as “data” the output of MCMC algorithms. Consider the trace plot above....continue reading.

Hi all, The paper “unbiased Markov chain Monte Carlo with couplings” co-written with John O’Leary and Yves Atchadé has been accepted as a read paper in JRSS: Series B, to...continue reading.

Hi all, This post describes how unbiased MCMC can help in approximating expectations with respect to “BayesBag”, an alternative to standard posterior distributions mentioned in Peter Bühlmann‘s discussion of Big...continue reading.

Hi all, Niloy Biswas (PhD student at Harvard) and I have recently arXived a manuscript on the assessment of MCMC convergence (using couplings!). Here I’ll describe the main result, and some...continue reading.

Hi all, This post is about some results from “Bias Properties of Budget Constrained Simulations“, by Glynn & Heidelberger and published in Operations Research in 1990. I have found these...continue reading.

Hi, Two years ago I blogged about couplings of conditional particle filters for smoothing.  The paper with Fredrik Lindsten and Thomas Schön has just been accepted for publication at JASA, and the arXiv...continue reading.

Hi, This post is about different ways of using Markov chain Monte Carlo (MCMC) algorithms for numerical integration or sampling. It can be a hard job to design an MCMC...continue reading.

Hi all, In this post, I’ll go through numerical experiments illustrating the scaling of some MCMC algorithms with respect to the dimension. I will focus on a simple setting, to...continue reading.