## Banff workshop [BIRS 12w5105 meeting [#2]]

**T**oday the program of 12w5105 was more on the theoretical side with adaptive MCMC in the morning and ABC in the afternoon. Éric Moulines and Gersende Fort shared a talk on two papers, one on adaptive tempering and the other one on equi-energy sampling, then Nando de Freitas spoke first about Gaussian process approximation for Bayesian optimisation, then about an adaptive Hamiltonian technique called Sardonics. And Jeff Rosenthal concluded the morning with a review of the results ensuring convergence for adaptive MCMC (with a delightful counter-example called Stairways to Heaven that reminded me of an ice climb in Utah!). After my talk, where Scott Sisson made an interesting comment on the difficulty to extend our framework to a large collection of models (since then the summary statistics have to differ), François Perron discussed in highly interesting details several approximation techniques for the Bayesian estimation of copulas and Scott Sisson presented his recent arXiv paper where a rough estimate of the joint posterior is obtained regression-adjustment ABC, and then estimates of each marginal posterior distribution are separately obtained in a lower-dimensional analysis, all this being connected with Bayes linear analysis. (I do not completely get the way summary statistics are selected for each marginal there, which seems to be done by hand. While I understand why using a lower-dimensional statistic helps in improving the approximation of the marginal posteriors and fights the curse of dimensionality, the fact that the joint posterior sample is based on different summary statistics for the different components makes an interesting statistical puzzle. Maybe the copula approach by François in the previous talk could be used at the final stage.) The final talk by Zhiqiang Tan on comparative performances of resampling and subsampling strategies generated a very animated discussion. (All talks being recorded, mine is available as an mp4 video but watch at your own peril!)

March 22, 2012 at 7:08 am

[…] the ice at all. There was a group of three climbers rappelling down as we arrived (at 2pm, after the morning talks!), and a couple of Australian climbers already on the second pitch (yes, there are Australian […]

March 21, 2012 at 3:22 pm

For the image analysis example I presented, we were only able to select the informative statistics for each marginal parameter “by hand” simply because we directly chose each statistic to be informative for one parameter only. E.g. measurements of dependence in the east-west direction are only likely to be informative for the east-west dependence parameter of the Gaussian random field etc.

Typically you won’t be able to do this, and will need to elicit your summary statistics using dimension reduction techniques (e.g. as in this paper *shameless plug*) for each marginal parameter in turn, though this should typically be fast to do.

Scott