Seminar in Nottingham

Last Thursday, I gave a seminar in Nottingham, the true birthplace of the Gibbs sampler!, and I had a quite enjoyable half-day of scientific discussions in the Department of Statistics, with a fine evening tasting a local ale in the oldest (?) inn in England (Ye Olde Trip to Jerusalem) and sampling Indian dishes at 4550 Miles [plus or minus epsilon, since the genuine distance is 4200 miles) from Dehli, plus a short morning run on the very green campus. In particular, I discussed with Theo Kypraios and Simon Preston parallel ABC and their recent paper in Statistics and Computing, their use of the splitting technique of Neiswanger et al. I discussed earlier but intended here towards a better ABC approximation since (a) each term in the product could correspond to a single observation and (b) hence no summary statistic was needed and a zero tolerance could be envisioned. The  paper discusses how to handle samples from terms in a product of densities, either by a Gaussian approximation or by a product of kernel estimates. And mentions connections with expectation propagation (EP), albeit not at the ABC level.

A minor idea that came to me during this discussion was to check whether or not a reparameterisation towards a uniform prior was a good idea: the plus of a uniform prior was that the power discussion was irrelevant, making both versions of the parallel MCMC algorithm coincide. The minus was not the computational issue since most priors are from standard families, with easily invertible cdfs, but rather why this was supposed to make a difference. When writing this on the train to Oxford, I started wondering as an ABC implementation is impervious to this reparameterisation. Indeed, simulate θ from π and pseudo-data given θ versus simulate μ from uniform and pseudo-data given T(μ) does not make a difference in the simulated pseudo-sample, hence in the distance selected θ’s, and still in one case the power does not matter while in the other case it does..!

Another discussion I had during my visit led me to conclude a bit hastily that a thesis topic I had suggested to a new PhD student a few months ago had already been considered locally and earlier, although it ended up as a different, more computational than conceptual, perspective (so not all was lost for my student!). In a wider discussion around lunch, we also had an interesting foray on possible alternatives to Bayes factors and their shortcomings, which was a nice preparation to my seminar on giving up posterior probabilities for posterior error estimates. And an opportunity to mention the arXival of a proper scoring rules paper by Phil Dawid, Monica Musio and Laura Ventura, related with the one I had blogged about after the Padova workshop. And then again about a connected paper with Steve Fienberg. This lunch discussion even included some (mild) debate about Murray Aitkin’s integrated likelihood.

As a completely irrelevant aside, this trip gave me the opportunity of a “pilgrimage” to Birmingham New Street train station, 38 years after “landing” for the first time in Britain! And to experience a fresco the multiple delays and apologies of East Midlands trains (“we’re sorry we had to wait for this oil train in York”, “we have lost more time since B’ham”, “running a 37 minutes delay now”, “we apologize for the delay, due to trespassing”, …), the only positive side being that delayed trains made delayed connections possible!