adaptive importance sampling

Bernard Delyon and François Portier arXived a paper last June on adaptive importance sampling. Among the early versions of this adaptive version, they quote Oh and Berger (1992), and West (1992), whose works we cited in our population Monte Carlo papers, but whose input I had forgotten when getting through this paper. The more vexing because Man-Suk Oh was a PhD student at Purdue when I was a postdoc there and we discussed about importance sampling on several occasions, and because Mike West had given his talk on using mixtures for importance purposes at my first Valencia meeting! Tuen Kloek and Herman van Dijk actually have an even earlier 1978 Econometrica paper on a two-stage version. The difficulty is of course in efficiently translating the requirement of updating the sampler in these different adaptive iterative versions…

“The theoretical properties of adaptive schemes are difficult to derive due to the recycling of the pastsamples at each stage and hence to the lack of independence between samples.” (p.2)

The goal of this paper is to look at convergence properties of some adaptive importance sampling when the total number of simulations grows to infinity. Plus, to provide a way to get rid of bad samples!