Archive for adaptive MCMC

Nature tidbits [and garbage out]

Posted in Books, Kids, Mountains, pictures, Travel, University life with tags , , , , , , , , , , , , , , , , , , , , , , , , , on October 25, 2024 by xi'an

Many bits of interest in the 25 July issue of Nature that stayed under a pile of journals for PNW reasons! Even though the cover is rather off-putting…

  • A call by the editors (and computer scientist Cal Newport) for scientists to “stop, drop, and think” (and the paperback version of Newport’s Slow Productivity has a nice cover that looks very much like Moraine Lake in Banff National Parc!)
  • Another call by a Science Po’ sociologist to the (then highly prospective) French government to increase research budget for French universities, which is not particularly original since this is a constant line on all unions’ desiderata, except for the argument that it would make a tuition fees increase more palatable, and to leave more freedom to researchers, with the oft-used argument that “fundamental research may have unexpected implications”. Except that a massive public deficit is going to impose budget squeezes in all spending lines of the Barnier government.
  • Worries of Indian and non-Indian demographers about the continued postponement of India’s national census, with the latest one dating from 2011. With strong repercussions on public policies, especially since the administrative data systems are rarely reliable. The article suggests that more than an estimated 100 million inhabitants are excluded from food subsidies as a consequence. This seems like an opportunity to develop open source alternatives that run the census from indirect observations, bypassing the reluctance of the Modi Government to launch the much delayed census. (Which could have been coupled with the electoral process earlier this year.)
  • An insight on four female “PhD influencers” from the Universities of Pennsylvania, Exeter, Hertfordshire, and Hong Kong (CUHK). Which has a plus side of exposing the life and interests of a PhD student. And a downside of being a social media product, with the many biases that come along posting to the general public.
  • A call for publishing more papers about negative results! Supporting (pre)registration of experiments.
  • A positive book review of The MANIAC of Benjamin Labatut around John von Neumann’s life, analysed by Karl Sigmund
  • A four-page long comment on the importance of preserving scientific US-China relations, despite the growing suspicion in the US that any scientific collaboration with Chinese institutions will benefit Chinese (State) interests. Without falling for a naive approach to such collaborations, and acknowledging the porous boundaries between fundamental and military research, one should acknowledge the great leap forward accomplished by Chinese universities in the past decade that set their researchers at the forefront of science in many fields.
  • A paper related with the cover on model collapse in AIs learning from AI-generated data. Just like MCMC learning a proposal from earlier simulations. A natural consequence of over-fitting.
  • Another paper on the phase (or quantum) transition of the two-dimensional Ising spin glass (model).
  • and the article on predatory conferences I already discussed in August.

re-MCM’d

Posted in Statistics, University life with tags , , , , , , , , , , , , , , , on June 28, 2023 by xi'an


When I entered the classroom on the Jussieu campus where the Monday morning session on PDMP was taking place, some friends told me a badge was waiting for me at the registration desk of MCM 2023! Most surprisingly since I had received a deregistration message a few weeks earlier. Great PDMP session with non-reversible tempering (warning: some PDMPs were harmed in the tempering process), scaling PDMPs for highly anisotropic targets, a PDMP form of reversible jump (with sticky floors!) and a more adaptive version of no-U turn via… PDMPs. After lunch at the nearby Grande Mosquée de Paris (I had not visited since… 1974!), I attended the slice sampler session, where mileage varied imho. With a take on doubly-intractable targets that did not seem to relate to the existing literature.

adaptive independent Metropolis-Hastings

Posted in Statistics with tags , , , , , , on May 8, 2018 by xi'an

When rereading this paper by Halden et al. (2009), I was reminded of the earlier and somewhat under-appreciated Gåsemyr (2003). But I find the convergence results therein rather counter-intuitive in that they seem to justify adaptive independent proposals with no strong requirement. Besides the massive Doeblin condition:

“The Doeblin condition essentially requires that all the proposal distribution [sic] has uniformly heavier tails than the target distribution.”

Even when the adaptation is based on an history vector made of rejected values and non-replicated accepted values. Actually  convergence of this sequence of adaptive proposals kernels is established under a concentration of the Doeblin constants a¹,a²,… towards one, in the sense that

E[(1-a¹)(1-a²)…]=0.

The reason may be that, with chains satisfying a Doeblin condition, there is a probability to reach stationarity at each step. Equal to a¹, a², … And hence to ignore adaptivity since each kernel keep the target π invariant. So in the end this is not so astounding. (The paper also reminded me of Wolfgang [or Vincent] Doeblin‘s short and tragic life.)

importance sampling with multiple MCMC sequences

Posted in Mountains, pictures, Statistics, Travel, University life with tags , , , , , , , , , , on October 2, 2015 by xi'an

Vivek Roy, Aixian Tan and James Flegal arXived a new paper, Estimating standard errors for importance sampling estimators with multiple Markov chains, where they obtain a central limit theorem and hence standard error estimates when using several MCMC chains to simulate from a mixture distribution as an importance sampling function. Just before I boarded my plane from Amsterdam to Calgary, which gave me the opportunity to read it completely (along with half a dozen other papers, since it is a long flight!) I first thought it was connecting to our AMIS algorithm (on which convergence Vivek spent a few frustrating weeks when he visited me at the end of his PhD), because of the mixture structure. This is actually altogether different, in that a mixture is made of unnormalised complex enough densities, to act as an importance sampler, and that, due to this complexity, the components can only be simulated via separate MCMC algorithms. Behind this characterisation lurks the challenging problem of estimating multiple normalising constants. The paper adopts the resolution by reverse logistic regression advocated in Charlie Geyer’s famous 1994 unpublished technical report. Beside the technical difficulties in establishing a CLT in this convoluted setup, the notion of mixing importance sampling and different Markov chains is quite appealing, especially in the domain of “tall” data and of splitting the likelihood in several or even many bits, since the mixture contains most of the information provided by the true posterior and can be corrected by an importance sampling step. In this very setting, I also think more adaptive schemes could be found to determine (estimate?!) the optimal weights of the mixture components.