Archive for University of Adelaide

Monte Carlo calculations of the radial distribution functions for a proton-electron plasma

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , on October 11, 2017 by xi'an

“In conclusion, the Monte Carlo method of calculating radial distribution functions in a plasma is a feasible approach if significant computing time is available (…) The results indicate that at least 10000 iterations must be completed before the system can be considered near to its equilibrium state, and for a badly chosen starting configuration, the run would need to be considerably longer (…) for more conclusive results a longer run is needed so that the energy of the system can settle into an equilibrium pattern and steady-state radial distribution functions can be obtained.” A.A. Barker

Looking for the history behind Barker’s formula the other day made me look for the original 1965 paper. Which got published in the Australian Journal of Physics at the beginning of Barker’s PhD at the University of Adelaide.

As shown in the above screenshot, the basis  of Barker’s algorithm is indeed Barker’s acceptance probability, albeit written in a somewhat confusing way since the current value of the chain is kept if a Uniform variate is smaller than what is actually the rejection probability. No mistake there! And more interestingly, Barker refers to Wood and Parker (1957) for the “complete and rigorous theory” behind the method. (Both Wood and Parker being affiliated with Los Alamos Scientific Laboratory, while Barker acknowledges support from both the Australian Institute of Nuclear Science and Engineering and the Weapons Research Establishment, Salisbury… This were times when nuclear weapon research was driving MCMC. Hopefully we will not come back to such times. Or, on the pessimistic side, we will not have time to come back to such times!)

As in Metropolis et al. (1953), the analysis is made on a discretised (finite) space, building the Markov transition matrix, stating the detailed balance equation (called microscopic reversibility). Interestingly, while Barker acknowledges that there are other ways of assigning the transition probability, his is the “most rapid” in terms of mixing. And equally interestingly, he discusses the scale of the random walk in the [not-yet-called] Metropolis-within-Gibbs move as major, targetting 0.5 as the right acceptance rate, and suggesting to adapt this scale on the go. There is also a side issue that is apparently not processed with all due rigour, namely the fact that the particles in the system cannot get arbitrarily close from one another. It is unclear how a proposal falling below this distance is processed by Barker’s algorithm. When implemented on 32 particles, this algorithm took five hours to execute 6100 iterations. With a plot of the target energy function that does not shout convergence, far from it! As acknowledged by Barker himself (p.131).

The above quote is from the conclusion and its acceptance of the need for increased computing times comes as a sharp contrast with this week when one of our papers was rejected based on this very feature..!

Barker at the Bernoulli factory

Posted in Books, Statistics with tags , , , , , , , on October 5, 2017 by xi'an

Yesterday, Flavio Gonçalves, Krzysztof Latuszýnski, and Gareth Roberts (Warwick) arXived a paper on Barker’s algorithm for Bayesian inference with intractable likelihoods.

“…roughly speaking Barker’s method is at worst half as good as Metropolis-Hastings.”

Barker’s acceptance probability (1965) is a smooth if less efficient version of Metropolis-Hastings. (Barker wrote his thesis in Adelaide, in the Mathematical Physics department. Most likely, he never interacted with Ronald Fisher, who died there in 1962) This smoothness is exploited by devising a Bernoulli factory consisting in a 2-coin algorithm that manages to simulate the Bernoulli variable associated with the Barker probability, from a coin that can simulate Bernoulli’s with probabilities proportional to [bounded] π(θ). For instance, using a bounded unbiased estimator of the target. And another coin that simulates another Bernoulli on a remainder term. Assuming the bound on the estimate of π(θ) is known [or part of the remainder term]. This is a neat result in that it expands the range of pseudo-marginal methods (and resuscitates Barker’s formula from oblivion!). The paper includes an illustration in the case of the far-from-toyish Wright-Fisher diffusion. [Making Fisher and Barker meeting, in the end!]

AMSI-SSAI Lecture #1 at University of Adelaide

Posted in pictures, Statistics, Travel, University life with tags , , , , on July 16, 2012 by xi'an

On Friday, I gave my first AMSI Lecture, at the University of Adelaide. The talk attracted a fair number of people, esp. when considering that I had already given a talk on ABC the day before. There also were several interesting questions at the end, mostly related to the (ABC) empirical likelihood part which seems to have a high power of attraction! This talk furthermore gave me the opportunity to visit the superb Ingkarni Wardli building housing math and engineering. This means “house of enquiry” in the local indigenous language, well-suited to a science building indeed! (My next talk is at UNSW on Monday afternoon, the very same talk I gave at the ASC 2012 conference last Thursday.)

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