## Adap’skiii [day 2]

**A**nother exciting day at Adap’skiii!!!

**Y**ves Atchadé presented a very recent work on the fundamental issue of estimating the asymptotic variance estimation for adaptive MCMC algorithms, with an intriguing experimental observation that a non-converging bandwidth with rate 1/n was providing better coverage than the converging rate. (I always found the issue of estimating the asymptotic variance both a tough problem and an important item in convergence assessment.) Galin Jones showed new regeneration results for componentwise MCMC samplers, with applications to quantile estimation. The iid structure produced by the regeneration mechanism allows rather naturally to introduce an adaptive improvement in those algorithms, if regeneration occurs often enough. (From the days of my Stat’Sci’ paper on convergence assessment, I love regeneration techniques for both theoretical and methodological reasons, even though they are often difficult to efficiently implement in practice.) Matti Vihola summarised several of his recent papers on the stability and convergence of adaptive MCMC algorithms, pursuing the Finnish tradition of leadership in adaptive algorithms! One point I found particularly interesting was the possibility of separating ergodicity from the Law of Large Numbers, thus reducing the constraints imposed by the containment condition. In the afternoon, Dawn Woodard discussed the convergence rate of the Gibbs sampler used for genomic motif discovery by Liu, Lawrence and Neuwald (1995). Scott Schmidler concluded the workshop by a far-ranging talk distinguishing between exploration and exploitation in adaptive MCMC algorithms, ie mixing vs burning, with illustrations using the Wang-Landau algorithm.

**T**hus, as in the previous editions of Adap’ski, we have had a uniformly high quality of talks about the current research in the area of adaptive algorithms (and a wee further). This shows the field is very well active and expanding, aiming at reaching a wider audience by providing verifiable convergence conditions and semi-automated softwares (like Jeff Rosenthal’s amcmc R code we used in ** Introducing Monte Carlo Methods with R**). Looking forward Adap’ski 4 (Adap’skiV?!), hopefully in Europe and why not in Chamonix?! Which could then lead us to call the next meeting Adap’skiX…

October 20, 2011 at 12:11 am

[…] submitted to the Annals of Applied Probability) a neat result on the Wang-Landau algorithm. (This algorithm, which modifies the target in a sort of reweighted partioned sampling to achieve faster […]

August 2, 2011 at 10:53 am

[…] papers session. Radu Craiu gave a talk on his Raptor algorithm, somehow connected to his talk in Utah last winter. This was an interesting example of adaptive MCMC, maybe the only one I will attend at JSM. In a […]

January 9, 2011 at 12:11 am

[…] now back home after five exciting and exhausting days in Park City, Utah! As reported earlier, the Adap’skiii meeting went on quite well, with high quality talks relating to edge research. I am thus completely […]