Archive for simulation

nested sampling: any prior anytime?!

Posted in Books, pictures, Statistics, Travel with tags , , , , , , , , , , , , on March 26, 2021 by xi'an

A recent arXival by Justin Alsing and Will Handley on “nested sampling with any prior you like” caught my attention. If only because I was under the impression that some priors would not agree with nested sampling. Especially those putting positive weight on some fixed levels of the likelihood function, as well as improper priors.

“…nested sampling has largely only been practical for a somewhat restrictive class of priors, which have a readily available representation as a transform from the unit hyper-cube.”

Reading from the paper, it seems that the whole point is to demonstrate that “any proper prior may be transformed onto the unit hypercube via a bijective transformation.” Which seems rather straightforward if the transform is not otherwise constrained: use a logit transform in every direction. The paper gets instead into the rather fashionable direction of normalising flows as density representations. (Which suddenly reminded me of the PhD dissertation of Rob Cornish at Oxford, which I examined last year. Even though nested was not used there in the same understanding.) The purpose appearing later (in the paper) or in fine to express a random variable simulated from the prior as the (generative) transform of a Uniform variate, f(U). Resuscitating the simulation from an arbitrary distribution from first principles.

“One particularly common scenario where this arises is when one wants to use the (sampled) posterior from one experiment as the prior for another”

But I remained uncertain at the requirement for this representation in implementing nested sampling as I do not see how it helps in bypassing the hurdles of simulating from the prior constrained by increasing levels of the likelihood function. It would be helpful to construct normalising flows adapted to the truncated priors but I did not see anything related to this version in the paper.

The cosmological application therein deals with the incorporation of recent measurements in the study of the ΛCDM cosmological model, that is, more recent that the CMB Planck dataset we played with 15 years ago. (Time flies, even if an expanding Universe!) Namely, the Baryon Oscillation Spectroscopic Survey and the SH0ES collaboration.

MCMC for conditional Bernoullis

Posted in Books, Statistics, University life with tags , , , , , on February 22, 2021 by xi'an

Jeremy Heng, Pierre Jacob [currently in Paris!] and Nianqiao Ju are in a recent arXival considering the simulation of a conditional Bernoulli, namely generating a vector of N Bernoullis with different probabilities under the constraint that their sum is fixed as I. Rather than going for a perfect simulator, with cost O(NI), they opt for the simplest of MCMC samplers, where a 0 and a 1 entries are exchanged at random. In connection with a recent spate of MCMC works using coupling, they establish convergence in O(N log N) steps, even when the probabilities are arbitrarily close to zero and one. Including the case when they are Uniformly generated. From a mundane perspective, I wonder at the appeal of using the probabilities to select the exchange pair. I realise sorting the probabilities is already of order O(N log N) avoiding selecting highly probable 1’s and highly probable 0’s should speed up converge, unless the gain is negligible. And to link MCMC and exact simulation in this setting, what would the cost of perfect sampling by sampling from the past be? Presumably much higher since there is little chance a total ordering can be found on the starting states.

data assimilation and reduced modelling for high-D problems [CIRM]

Posted in Books, Kids, Mountains, pictures, Running, Statistics, University life with tags , , , , , , , , , , , , , , , , , on February 8, 2021 by xi'an

Next summer, from 19 July till 27 August, there will be a six week program at CIRM on the above theme, bringing together scientists from both the academic and industrial communities. The program includes a one-week summer school followed by 5 weeks of research sessions on projects proposed by academic and industrial partners.

Confirmed speakers of the summer school (Jul 19-23) are:

  • Albert Cohen (Sorbonne University)
  • Masoumeh Dashti (University of Sussex)
  • Eric Moulines (Ecole Polytechnique)
  • Anthony Nouy (Ecole Centrale de Nantes)
  • Claudia Schillings (Mannheim University)

Junior participants may apply for fellowships to cover part or the whole stay. Registration and application to fellowships will be open soon.

unbiased estimator of determinant

Posted in Books, Statistics with tags , , , , on July 3, 2020 by xi'an

Just saw this new [one page] posting on arXiv, meaning an unbiased estimate of the determinant can be derived much faster. If less reliably. This trick can be helpful for (pseudo-marginal) MCMC steps when the determinant itself is of limited interest… (The importance version is not truly needed!)

data science [down] under the hood [webinar]

Posted in Statistics with tags , , , , , , on June 21, 2020 by xi'an