Archive for Markov chain Monte Carlo algorithm

MCqMC 2020 live and free and online

Posted in pictures, R, Statistics, Travel, University life with tags , , , , , , , , , , , , , on July 27, 2020 by xi'an

The MCqMC 20202 conference that was supposed to take place in Oxford next 9-14 August has been turned into an on-line free conference since travelling remains a challenge for most of us. Tutorials and plenaries will be live with questions  on Zoom, with live-streaming and recorded copies on YouTube. They will probably be during 14:00-17:00 UK time (GMT+1),  15:00-18:00 CET (GMT+2), and 9:00-12:00 ET. (Which will prove a wee bit of a challenge for West Coast and most of Asia and Australasia researchers, which is why our One World IMS-Bernoulli conference we asked plenary speakers to duplicate their talks.) All other talks will be pre-recorded by contributors and uploaded to a website, with an online Q&A discussion section for each. As a reminder here are the tutorials and plenaries:

Invited plenary speakers:

Aguêmon Yves Atchadé (Boston University)
Jing Dong (Columbia University)
Pierre L’Écuyer (Université de Montréal)
Mark Jerrum (Queen Mary University London)
Peter Kritzer (RICAM Linz)
Thomas Muller (NVIDIA)
David Pfau (Google DeepMind)
Claudia Schillings (University of Mannheim)
Mario Ullrich (JKU Linz)

Tutorials:

Fred Hickernell (IIT) — Software for Quasi-Monte Carlo Methods
Aretha Teckentrup (Edinburgh) — Markov chain Monte Carlo methods

unbiased MCMC discussed at the RSS tomorrow night

Posted in Books, Kids, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , on December 10, 2019 by xi'an

The paper ‘Unbiased Markov chain Monte Carlo methods with couplings’ by Pierre Jacob et al. will be discussed (or Read) tomorrow at the Royal Statistical Society, 12 Errol Street, London, tomorrow night, Wed 11 December, at 5pm London time. With a pre-discussion session at 3pm, involving Chris Sherlock and Pierre Jacob, and chaired by Ioanna Manolopoulou. While I will alas miss this opportunity, due to my trip to Vancouver over the weekend, it is great that that the young tradition of pre-discussion sessions has been rekindled as it helps put the paper into perspective for a wider audience and thus makes the more formal Read Paper session more profitable. As we discussed the paper in Paris Dauphine with our graduate students a few weeks ago, we will for certain send one or several written discussions to Series B!

what if what???

Posted in Books, Statistics with tags , , , , , on October 7, 2019 by xi'an

[Here is a section of the Wikipedia page on Monte Carlo methods which makes little sense to me. What if it was not part of this page?!]

Monte Carlo simulation versus “what if” scenarios

There are ways of using probabilities that are definitely not Monte Carlo simulations – for example, deterministic modeling using single-point estimates. Each uncertain variable within a model is assigned a “best guess” estimate. Scenarios (such as best, worst, or most likely case) for each input variable are chosen and the results recorded.[55]

By contrast, Monte Carlo simulations sample from a probability distribution for each variable to produce hundreds or thousands of possible outcomes. The results are analyzed to get probabilities of different outcomes occurring.[56] For example, a comparison of a spreadsheet cost construction model run using traditional “what if” scenarios, and then running the comparison again with Monte Carlo simulation and triangular probability distributions shows that the Monte Carlo analysis has a narrower range than the “what if” analysis. This is because the “what if” analysis gives equal weight to all scenarios (see quantifying uncertainty in corporate finance), while the Monte Carlo method hardly samples in the very low probability regions. The samples in such regions are called “rare events”.

normal variates in Metropolis step

Posted in Books, Kids, R, Statistics, University life with tags , , , , , , , , on November 14, 2017 by xi'an

A definitely puzzled participant on X validated, confusing the Normal variate or variable used in the random walk Metropolis-Hastings step with its Normal density… It took some cumulated efforts to point out the distinction. Especially as the originator of the question had a rather strong a priori about his or her background:

“I take issue with your assumption that advice on the Metropolis Algorithm is useless to me because of my ignorance of variates. I am currently taking an experimental course on Bayesian data inference and I’m enjoying it very much, i believe i have a relatively good understanding of the algorithm, but i was unclear about this specific.”

despite pondering the meaning of the call to rnorm(1)… I will keep this question in store to use in class when I teach Metropolis-Hastings in a couple of weeks.

Bouncing bouncy particle papers

Posted in Books, pictures, Statistics, University life with tags , , , , on July 27, 2017 by xi'an

Yesterday, two papers on bouncy particle samplers simultaneously appeared on arXiv, arxiv:1707.05200 by Chris Sherlock and Alex Thiery, and arxiv:1707.05296 by Paul Vanetti, Alexandre Bouchard-Côté, George Deligiannidis, and Arnaud Doucet. As a coordinated move by both groups of authors who had met the weeks before at the Isaac Newton Institute in Cambridge.

The paper by Sherlock and Thiery, entitled a discrete bouncy particle sampler, considers a delayed rejection approach that only requires point-wise evaluations of the target density. The delay being into making a speed flip move after a proposal involving a flip in the speed and a drift in the variable of interest is rejected. To achieve guaranteed ergodicity, they add a random perturbation as in our recent paper, plus another perturbation based on a Brownian argument. Given that this is a discretised version of the continuous-time bouncy particle sampler, the discretisation step δ need be calibrated. The authors follow a rather circumvoluted argument to argue in favour of seeking a maximum number of reflections (for which I have obviously no intuition). Overall, I find it hard to assess how much of an advance this is, even when simulations support the notion of a geometric convergence.

“Our results provide a cautionary example that in certain high-dimensional scenarios, it is still preferable to perform refreshment even when randomized bounces are used.” Vanetti et al.

The paper by Paul Vanetti and co-authors has a much more ambitious scale in that it unifies most of the work done so far in this area and relates piecewise deterministic processes, Hamiltonian Monte Carlo, and discrete versions, containing on top fine convergence results. The main idea is to improve upon the existing deterministic methods by taking (more) into account the target density. Hence the use of a bouncy particle sampler associated with the Hamiltonian (as in HMC). This borrows from an earlier slice sampler idea of Iain Murray, Ryan Adams, and David McKay (AISTATS 2010), exploiting an exact Hamiltonian dynamics for an approximation to the true target to explore its support. Except that bouncing somewhat avoids the slice step. The [eight] discrete bouncy particle particle samplers derived from this framework are both correct against the targeted distribution and do not require the simulation of event times. The paper distinguishes between global and local versions, the later exploiting conditional independence properties in the (augmented) target. Which sounds like a version of multiple slice sampling.