sticky Metropolis

My former student Roberto Casarin and his colleagues wrote (and arXived) a paper entitled Adaptive sticky generalized Metropolis algorithm. The basic idea is to use some of the rejected and past values of the chain to build an adaptive proposal, the criterion for choosing those values being related with the distance at the rejected point between the target and the proposal. In a sense, it gives a reward to surprising points, i.e. points where the proposal does poorly in approximating the target. On top of this, they include a multiple-try strategy where several values are generated from the current proposal and one of them is selected, to be accepted or rejected in a Metropolis step. The learning set may include several of the proposed (and rejected) values. This paper generalises Holden, Hauge and Holden (AoAP, 2009) and extends their proof of stationarity. The authors explore at length (the paper is 63 pages long!) the construction of the adaptive proposal distribution. This construction appears to be quite similar to Gilks’ and Wild’s (1993) ARMS algorithm. Hence, unless I missed a generalisation, it seems to me that the solutions are restricted to unidimensional settings. For instance, the authors propose to implement their algorithm for each complex conditional in a Gibbs sampler, meaning starting from scratch and running a large enough number of iterations to “reach” convergence. I also wonder at the correspondence between this construction and the original assumption of a minorisation condition wrt the target density in the event of an unbounded support. While this paper represents an interesting extension of the automated simulation algorithms of the ARMS type, and while the method is investigated thoroughly by several simulation experiments (in the second half of the paper), I remain somehow circumspect at the possibly of using ASMTM in complex high-dimensional problems as the learning cost soar with the dimension.

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