## Fusion at CIRM

Posted in Mountains, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , on October 24, 2022 by xi'an

Today is the first day of the FUSION workshop Rémi Bardenet and myself organised. Due to schedule clashes, I will alas not be there, since [no alas!] at the BNP conference in Chili. The program and collection of participants is quite exciting and I hope more fusion will result from this meeting. Enjoy! (And beware of boars, cold water, and cliffs!!!)

## likelihood-free nested sampling

Posted in Books, Statistics with tags , , , , , , on April 11, 2022 by xi'an

Last week, I came by chance across a paper by Jan Mikelson and Mustafa Khammash on a likelihood-free version of nested sampling (a popular keyword on the ‘Og!). Published in 2020 in PLoS Comput Biol. The setup is a parameterised and hidden state-space model, which allows for an approximation of the (observed) likelihood function L(θ|y) by means of a particle filter. An immediate issue with this proposal is that a novel  filter need be produced for a new value of the parameter θ, which makes it enormously expensive. It then gets more bizarre as the [Monte Carlo] distribution of the particle filter approximation ô(θ|y) is agglomerated with the original prior π(θ) as a joint “prior” [despite depending on the observed y] and a nested sampling is conducted with level sets of the form

ô(θ|y)>ε.

Actually, if the Monte Carlo error was null, that is, if the number of particles was infinite,

ô(θ|y)=L(θ|y)

implies that this is indeed the original nested sampler. Simulation from the restricted region is done by constructing an extra density estimator of the constrained distribution (in θ)…

“We have shown how using a Monte Carlo estimate over the livepoints not only results in an unbiased estimator of the Bayesian evidence Z, but also allows us to derive a formulation for a lower bound on the achievable variance in each iteration (…)”

As shown by the above the authors insist on the unbiasedness of the particle approximation, but since nested sampling is not producing an unbiased estimator of the evidence Z, the point is somewhat moot. (I am also rather surprised by the reported lack of computing time benefit in running ABC-SMC.)

## no filter [no jatp]

Posted in Kids, Mountains, pictures with tags , , , , , , , , , , , on September 14, 2020 by xi'an

## IMS workshop [day 4]

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , on August 31, 2018 by xi'an

While I did not repeat the mistake of yesterday morning, just as well because the sun was unbearably strong!, I managed this time to board a bus headed in the wrong direction and as a result went through several remote NUS campi! Missing the first talk of the day as a result. By Youssef Marzouk, with a connection between sequential Monte Carlo and optimal transport. Transport for sampling, that is. The following talk by Tiangang Cui was however related, with Marzouk a co-author, as it aimed at finding linear transforms towards creating Normal approximations to the target to be used as proposals in Metropolis algorithms. Which may sound like something already tried a zillion times in the MCMC literature, except that the setting was rather specific to some inverse problems, imposing a generalised Normal structure on the transform, then optimised by transport arguments. It is unclear to me [from just attending the talk] how complex this derivation is and how dimension steps in, but the produced illustrations were quite robust to an increase in dimension.

The remaining talks for the day were mostly particular, from Anthony Lee introducing a new and almost costless way of producing variance estimates in particle filters, exploiting only the ancestry of particles, to Mike Pitt discussing the correlated pseudo-marginal algorithm developed with George Deligiannidis and Arnaud Doucet. Which somewhat paradoxically managed to fight the degeneracy [i.e., the need for a number of terms increasing like the time index T] found in independent pseudo-marginal resolutions, moving down to almost log(T)… With an interesting connection to the quasi SMC approach of Mathieu and Nicolas. And Sebastian Reich also stressed the links with optimal transport in a talk about data assimilation that was way beyond my reach. The day concluded with fireworks, through a magistral lecture by Professeur Del Moral on a continuous time version of PMCMC using the Feynman-Kac terminology. Pierre did a superb job during his lecture towards leading the whole room to the conclusion.

## unbiased consistent nested sampling via sequential Monte Carlo [a reply]

Posted in pictures, Statistics, Travel with tags , , , , , , , , on June 13, 2018 by xi'an

Rob Salomone sent me the following reply on my comments of yesterday about their recently arXived paper.

Our main goal in the paper was to show that Nested Sampling (when interpreted a certain way) is really just a member of a larger class of SMC algorithms, and exploring the consequences of that. We should point out that the section regarding calibration applies generally to SMC samplers, and hope that people give those techniques a try regardless of their chosen SMC approach.
Regarding your question about “whether or not it makes more sense to get completely SMC and forego any nested sampling flavour!”, this is an interesting point. After all, if Nested Sampling is just a special form of SMC, why not just use more standard SMC approaches? It seems that the Nested Sampling’s main advantage is its ability to cope with problems that have “phase transition’’ like behaviour, and thus is robust to a wider range of difficult problems than annealing approaches. Nevertheless, we hope this way of looking at NS (and showing that there may be variations of SMC with certain advantages) leads to improved NS and SMC methods down the line.
Regarding your post, I should clarify a point regarding unbiasedness. The largest likelihood bound is actually set to infinity. Thus, for the fixed version of NS—SMC, one has an unbiased estimator of the “final” band. Choosing a final band prematurely will of course result in very high variance. However, the estimator is unbiased. For example, consider NS—SMC with only one strata. Then, the method reduces to simply using the prior as an importance sampling distribution for the posterior (unbiased, but often high variance).