t-walk on the banana side

Following my remarks on the t-walk algorithm in the recent A General Purpose Sampling Algorithm for Continuous Distributions, published by Christen and Fox in Bayesian Analysis that acts like a general purpose MCMC algorithm, Darren Wraith tested it on the generic (10 dimension) banana target we used in the cosmology paper. Here is an output from his comparison R program:

The use of the t-walk algorithm (left, with the same number of particles) in this very special case thus produces a wider variability  on the estimated means than the use of adaptive MCMC (center) and our (tuned) PMC algorithm (right).

5 Responses to “t-walk on the banana side”

  1. The t-walk implementations are available in various languages (R, Python, etc.). Is implementation for the PMC sampler available? I haven’t found a link (checked also the arXiv paper). Thanks for the comparison!

  2. Thank you for the attention received to our paper

    Yes, the first phrase in our paper is:

    “We develop a new general purpose MCMC sampler for arbitrary continuous distributions that requires no tuning.”

    Does it mix as well as a fine tune purpose made algorithm?
    Of course not. Does it *always* work well?
    We also say, in the second par. of the discussion section:

    “However, we have found an example in which extremely high
    correlations in a high-dimensional problem lead to very slow mixing of the t-walk. ”

    In the example above, the t-walk should need a far bigger sample size.
    I suppose also that the t-walk and the AMC were simpler and
    faster to program. That is the idea of generic algorithms; but indeed,
    there should be examples in which purpose made algorithms
    result in better mixing than generic algorithms like the t-walk.

    • My point was that the PMC is also an all-purpose generic algorithm. In short, I do not believe there is such a thing as an algorithm that works in all situations with no tuning whatsoever, this is the reason why I reacted at the first sentence I read from the paper…

  3. Thanks for comparison (and comments in your previous post)! I think there should be possibility to post comments and comparisons like these directly on the journal website. Now it is possible that many reading the t-walk paper don’t find this useful comparison…

    • Thanks. The idea of posting comments and analyses on BA is something I suggested a while ago to Brad Carlin but he did not want to mix the journal with a blog. I wish I had time to organise such a blog aggregating all comments…

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