Archive for Italia
Chris Drovandi (QUT) sent me his impression on BISP8 that just took place in Milano, Italia (BISP stands for Bayesian inference in stochastic processes):
Here is a review of some of the talks at BISP8. For the other talks I do not have sufficient background to give the talks the justice that they deserve. It was a very enjoyable small workshop with many talks in my areas of interest.
In the first session Vanja Dukic presented bayesian inference of SEIR epidemic DE models and state space models of google flu trends data. In the case of the state space models a particle learning algorithm was developed. The author considered both fixed and random effects for the data in each US state. In the second session, Murali Haran presented a likelihood-free approach for inferring the parameters of a spatio-temporal epidemic model. The speaker used a Gaussian process emulator of the model based on model simulations from a regulator grid of parameter values. The emulator approach is suggested to be less intensive in terms of the number of model simulations compared with abc but is only suitable for low dimensional inference problems (even less so than abc).
In the first session of day 2 Ana Palacios combined the gompertz model with Markov processes to create flexible and realistic stochastic growth models. The resulting model has a difficult likelihood and inference was performed by completing the likelihood creating simple Gibbs moves and by ABC.
There were 3 talks in a row on inference for SDEs. The first, by Simon Särkkä, avoids evaluating an intractable transition density by proposing from another diffusion model and computing importance weights using the girsanov theorem. Next, Samuel Kou used a population MCMC type approach where each chain had a different Euler discretisation. This helps improve mixing for the chain with the finest grid. Moves between chains are complicated by the different dimension for each chain. The author used a filling approach to overcome this. A very interesting aspect of the talk was using information from all chains to extrapolate various posterior quantiles to delta_t is 0 (no discretisation implying the correct posterior). I assume the extrapolation may not work as well for the extreme quantiles. The third talk, by Andrew Golightly, proposed an auxiliary approach to improve PMCMC for these models. This talk was the most technical (for me) so need more time to digest. Following my talk (based on some work here. And some current work.) was an applied talk using smc2 methodology.
On the final day Alexandros Beskos investigated the use of SMC for Bayesian inference for a high dimensional (static) parameter. SMC is advocated here due to the ease of adaptation relative to MCMC when there is no structure in the model. The base of the approach I believe was that of Chopin (2002).
Here are the slides of my talk in Padova for the workshop Recent Advances in statistical inference: theory and case studies (very similar to the slides for the Varanasi and Gainesville meetings, obviously!, with Peter Müller commenting [at last!] that I had picked the wrong photos from Khajuraho!)
The worthy Padova addendum is that I had two discussants, Stefano Cabras from Universidad Carlos III in Madrid, whose slides are :
and Francesco Pauli, from Trieste, whose slides are:
These were kind and rich discussions with many interesting openings: Stefano’s idea of estimating the pivotal function h is opening new directions, obviously, as it indicates an additional degree of freedom in calibrating the method. Esp. when considering the high variability of the empirical likelihood fit depending on the the function h. For instance, one could start with a large collection of candidate functions and build a regression or a principal component reparameterisation from this collection… (Actually I did not get point #1 about ignoring f: the empirical likelihood is by essence ignoring anything outside the identifying equation, so as long as the equation is valid..) Point #2: Opposing sample free and simulation free techniques is another interesting venue, although I would not say ABC is “sample free”. As to point #3, I will certainly get a look at Monahan and Boos (1992) to see if this can drive the choice of a specific type of pseudo-likelihoods. I like the idea of checking the “coverage of posterior sets” and even more “the likelihood must be the density of a statistic, not necessarily sufficient” as it obviously relates with our current ABC model comparison work… Esp. when the very same paper is mentioned by Francesco as well. Grazie, Stefano! I also appreciate the survey made by Francesco on the consistency conditions, because I think this is an important issue that should be taken into consideration when designing ABC algorithms. (Just pointing out again that, in the theorem of Fearnhead and Prangle (2012) quoting Bernardo and Smith (1992), some conditions are missing for the mathematical consistency to apply.) I also like the agreement we seem to reach about ABC being evaluated per se rather than an a poor man’s Bayesian method. Francesco’s analysis of Monahan and Boos (1992) as validating or not empirical likelihood points out a possible link with the recent coverage analysis of Prangle et al., discussed on the ‘Og a few weeks ago. And an unsuspected link with Larry Wasserman! Grazie, Francesco!