Archive for Queensland University of Technology

Nested Sampling SMC [a reply]

Posted in Books, Statistics, University life with tags , , , , , , , , , on April 9, 2020 by xi'an
Here is a response from Robert Salomone following my comments of the earlier day (and pointing out I already commented the paper two years ago):
You may be interested to know that we are at the tail end of carrying out a major revision of the paper, which we hope will be done in the near future — there will be some new theory (we are in the final stages for a consistency proof of the ANS-SMC algorithm with new co-author Adam Johansen), as well as new numerics (including comparisons to Nested Sampling), and additional discussion that clarifies the overall narrative.
A few comments relating your post that may clear some things up:
  • The method you describe with the auxiliary variable is actually one of three proposed algorithms. We call this one “Improved Nested Sampling” as it is the algorithm most similar to the original Nested Sampling. Two further extensions are the adaptive SMC sampler, and the fixed SMC sampler – the latter of which is provably consistent and unbiased for the model evidence (we also often see improvements over standard NS for similar computational effort when MCMC is used).
  • Regarding computational effort – it is the same for Improved NS (in fact, you can obtain the standard Nested Sampling evidence estimate from the same computational run!). For the adaptive variant, the computational effort is roughly the same for ρ = e⁻¹. In the current version of the paper this is only discussed briefly (last page of p.23). However, in the revision we will include additional experiments comparing the practical performance.
  • Regarding the question of “why not regular SMC”; we chose to focus more on why SMC is a good way to do Nested Sampling rather than why Nested Sampling is a good way to do SMC. Our main priority was to show there is a lot of opportunity to develop new nested sampling style algorithms by approaching it from a different angle. That said, Nested Sampling’s primary advantage over standard SMC seems to be in problems involving “phase transitions’’ such as our first example, for which temperature based methods are inherently ill-suited (and will often fail to detect so!).

nested sampling via SMC

Posted in Books, pictures, Statistics with tags , , , , , , , , , , , , on April 2, 2020 by xi'an

“We show that by implementing a special type of [sequential Monte Carlo] sampler that takes two im-portance sampling paths at each iteration, one obtains an analogous SMC method to [nested sampling] that resolves its main theoretical and practical issues.”

A paper by Queenslander Robert Salomone, Leah South, Chris Drovandi and Dirk Kroese that I had missed (and recovered by Grégoire after we discussed this possibility with our Master students). On using SMC in nested sampling. What are the difficulties mentioned in the above quote?

  1. Dependence between the simulated samples, since only the offending particle is moved by one or several MCMC steps. (And MultiNest is not a foolproof solution.)
  2. The error due to quadrature is hard to evaluate, with parallelised versions aggravating the error.
  3. There is a truncation error due to the stopping rule when the exact maximum of the likelihood function is unknown.

Not mentioning the Monte Carlo error, of course, which should remain at the √n level.

“Nested Sampling is a special type of adaptive SMC algorithm, where weights are assigned in a suboptimal way.”

The above remark is somewhat obvious for a fixed sequence of likelihood levels and a set of particles at each (ring) level. moved by a Markov kernel with the right stationary target. Constrained to move within the ring, which may prove delicate in complex settings. Such a non-adaptive version is however not realistic and hence both the level sets and the stopping rule need be selected from the existing simulation, respectively as a quantile of the observed likelihood and as a failure to modify the evidence approximation, an adaptation that is a Catch 22! as we already found in the AMIS paper.  (AMIS stands for adaptive mixture importance sampling.) To escape the quandary, the authors use both an auxiliary variable (to avoid atoms) and two importance sampling sequences (as in AMIS). And only a single particle with non-zero incremental weight for the (upper level) target. As the full details are a bit fuzzy to me, I hope I can experiment with my (quarantined) students on the full implementation of the method.

“Such cases asides, the question whether SMC is preferable using the TA or NS approach is really one of whether it is preferable to sample (relatively) easy distributions subject to a constraint or to sample potentially difficult distributions.”

A question (why not regular SMC?) I was indeed considering until coming to the conclusion section but did not find it treated in the paper. There is little discussion on the computing requirements either, as it seems the method is more time-consuming than a regular nested sample. (On the personal side,  I appreciated very much their “special thanks to Christian Robert, whose many blog posts on NS helped influence this work, and played a large partin inspiring it.”)

positions at QUT stats

Posted in Statistics with tags , , , , , , , , on September 4, 2017 by xi'an

Chris Drovandi sent me the information that the Statistics GroupQUT, Brisbane, is advertising for three positions:

This is a great opportunity, a very active group, and a great location, which I visited several times, so if interested apply before October 1.

Bayes on the beach [and no bogus!]

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , on July 27, 2016 by xi'an

Bayes on the Beach is a yearly conference taking place in Queensland Gold Coast and organised by Kerrie Mengersen and her BRAG research group at QUT. To quote from the email I just received, the conference will be held at the Mantra Legends Hotel on Surfers Paradise, Gold Coast during November 7 – 9, 2016. The conference provides a forum for discussion on developments and applications of Bayesian statistics, and includes keynote presentations, tutorials, practical problem-based workshops, invited oral presentations, and poster presentations. Abstract submissions are now open until September 2.

Xi’an Australian Tour 2012

Posted in Running, Statistics, Travel, University life with tags , , , , , , , , , , on May 25, 2012 by xi'an

Here is my schedule (so far) for my Australian trip this summer/winter… Looking forward meeting loads of interesting people, problems and places!

Tour Schedule

Date Host Institution Venue Time Title
12 July Australian Statistical Conference Meeting Room 11 9:30 am Approximate Bayesian Computation for model selection
13 July University of Adelaide TBC TBC TBC
16 July University of NSW Via AGR 2 pm ABC methods for Bayesian model choice
17 July University of Western Sydney TBC TBC Rao-Blackwellisation of sampling schemes
26 July University of Melbourne Russell Love theatre, Richard Berry (Bldg 160) 2 pm Approximate Bayesian computation (ABC): advances and limitations
26 July AMSI Public Lecture TBC
6 pm Simulation as a universal tool for statistics
27 July Monash University, Econometrics and Business Statistics seminar TBC
2 pm ABC methods for Bayesian model choice
14 August Australian National University Seminar Room G35, John Dedman (Bldg 27) 2 pm Approximate Bayesian computation (ABC): advances and limitations
15 August University of Wollongong CSSM Meeting (Goulburn) Rao-Blackwellisation of sampling schemes
20 August University of Queensland Room N201, Building 50 2 pm Rao-Blackwellisation of sampling schemes
21 August Queensland University of Technology GP-Z1064 Gibson Room TBC ABC methods for Bayesian model choice
21 August Queensland University of Technology GP-Z1064 Gibson Room TBC
Simulation as a universal tool for statistics