When I read in the abstract of the recent A General Purpose Sampling Algorithm for Continuous Distributions, published by Christen and Fox in Bayesian Analysis that
We develop a new general purpose MCMC sampler for arbitrary continuous distributions that requires no tuning.
I am slightly bemused. The proposal of the authors is certainly interesting and widely applicable but to cover arbitrary distributions in arbitrary dimensions with no tuning and great performances sounds too much like marketing on steroids! The 101 Theorem in MCMC methods is that, no matter how good your sampler is, there exists an exotic distribution out there whose only purpose is to make it crash!
The algorithm in A General Purpose Sampling Algorithm for Continuous Distributions is based on two dual and coupled chains which are used towards a double target . Given that only one of the two chains moves at each iteration, according to a random walk, there is a calibration parameter that definitely influences the performances of the method, if not the acceptance probability. This multiple chain approach is reminding me both of coupled schemes developed by Gareth Roberts in the late 1990′s, along with Laird Breyer, in the wake of the perfect sampling “revolution” and of delayed rejection sampling, as proposed by Antonietta Mira in those years as well. However, there is no particular result in the paper showing an improvement in convergence time over more traditional samplers. (In fact, the random walk nature of the algorithm strongly suggests a lack of uniform ergodicity.) The paper only offers a comparison with an older optimal scaled random walk proposal of Roberts and Rosenthal (Statistical Science, 2001). Rather than with the more recent and effective adaptive Metropolis-Hastings algorithm developed by the same authors.
Since the authors developed a complete set of computer packages, including one in R, I figure people will start to test the method to check for possible improvement over the existing solutions. If the t-walk is indeed superior sui generis, we should hear more about it in the near future…