In a recent arXival, Blazej Miasojedow, Wojciech Niemiro and Wojciech Rejchel establish the convergence of a maximum likelihood estimator based on an MCMC approximation of the likelihood function. As in intractable normalising constants. The main result in the paper is a Central Limit theorem for the M³C²L estimator that incorporates an additional asymptotic variance term for the Monte Carlo error. Where both the sample size n and the number m of simulations go to infinity. Independently so. However, I do not fully perceive the relevance of using an MCMC chain to target an importance function [which is used in the approximation of the normalising constant or otherwise for the intractable likelihood], relative to picking an importance function h(.) that can be directly simulated.Archive for Vancouver Island
asymptotics of M³C²L
Posted in Statistics with tags asymptotics, fog, maximum likelihood estimation, M³C²L, Monte Carlo Statistical Methods, Pacific North West, Tofino, Vancouver Island on August 19, 2018 by xi'anIn a recent arXival, Blazej Miasojedow, Wojciech Niemiro and Wojciech Rejchel establish the convergence of a maximum likelihood estimator based on an MCMC approximation of the likelihood function. As in intractable normalising constants. The main result in the paper is a Central Limit theorem for the M³C²L estimator that incorporates an additional asymptotic variance term for the Monte Carlo error. Where both the sample size n and the number m of simulations go to infinity. Independently so. However, I do not fully perceive the relevance of using an MCMC chain to target an importance function [which is used in the approximation of the normalising constant or otherwise for the intractable likelihood], relative to picking an importance function h(.) that can be directly simulated.little people of Tofino [jatp]
Posted in Kids, pictures, Running, Travel with tags British Columbia, jatp, little people, Tofino, tree, vacations, Vancouver Island on August 19, 2018 by xi'an
optimal approximations for importance sampling
Posted in Mountains, pictures, Statistics, Travel with tags British Columbia, cross validated, importance sampling, Lone Cone Mountain, Meares Island, minimum variance, Monte Carlo Statistical Methods, multiple importance methods, optimisation, Tofino, Vancouver Island, zero variance importance sampling on August 17, 2018 by xi'an
“…building such a zero variance estimator is most of the times not practical…”
As I was checking [while looking at Tofino inlet from my rental window] on optimal importance functions following a question on X validated, I came across this arXived note by Pantaleoni and Heitz, where they suggest using weighted sums of step functions to reach minimum variance. However, the difficulty with probability densities that are step functions is that they necessarily have a compact support, which thus make them unsuitable for targeted integrands with non-compact support. And making the purpose of the note and the derivation of the optimal weights moot. It points out its connection with the reference paper of Veach and Guibas (1995) as well as He and Owen (2014), a follow-up to the other reference paper by Owen and Zhou (2000).
impressions soleil levant [jatp]
Posted in Mountains, pictures, Running, Travel with tags Balmoral Beach, British Columbia, Canada, Claude Monet, Comox, forest fire, Georgia Strait, jatp, Pacific Ocean, smog, sunrise, Vancouver Island on August 14, 2018 by xi'an
off to Vancouver
Posted in Mountains, pictures, Running, Statistics, Travel, University life with tags Bayesian Analysis, British Columbia, Canada, default prior, Joint Statistical Meeting, JSM 2018, mixture of distributions, objective Bayes, summer of British conferences, Vancouver Island on July 29, 2018 by xi'an
I am off today to Vancouver for JSM2018, eight years after I visited the West Coast for another JSM! And a contender for the Summer of British Conferences, since it is in British Columbia.
And again looking forward the city, (some of) the meeting, and getting together with long-time-no-see friends. Followed by a fortnight of vacations on Vancouver Island where ‘Og posting may get sparse…
I hope I can take advantage of the ten hours in the plane from Paris to write my talk from scratch about priors for mixtures of distributions. Based on our papers with Clara Grazian and with Kaniav Kamary and Kate Lee. Still having some leeway since my talk is on Thursday morning, on the last day of the meeting…
