Is the algorithm in 'Transport map accelerated Markov chain Monte Carlo' included?

Question

Hi

I was wondering if there is any tutorial on how to set up a setting simialr to "Transport preconditioned MCMC' similar to [1]. I checked the tutorial but it doesn't seem any of those are related.

f that setting is possible with TransportMaps, I would be thankful if you provide an tutorial or some advice.

[1] Matthew Parno and Youssef Marzouk. Transport map accelerated Markov chain Monte Carlo. submitted, pages 1–50, 2014. 

Answer 1

The transport preconditioned MCMC can be coded using TransportMaps. There is not a tutorial page for that yet, but the idea is to construct (inverse) maps from MCMC samples to then precondition new chains. The package TransportMaps provides very few Markov Chain samplers (standard ones like Metropolis-Hastings and some Gibbs variations). More samplers are available through MUQ, which also implements the construction of transport maps from samples (only polynomial ones which don't enforce monotonicity everywhere though). I will push to include a tutorial on this technique once I'm back.

Comments

Thanks a lot.

I will try this algorithm by myself firstly.

Best,

Aaron

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hi Aaron,

btw, I know that the MUQ developers are hoping to implement monotone transport parameterizations in MUQ (e.g., using the integrated-squared approach in the TranportMaps package) in the next few months. Then the map-accelerated MCMC algorithm in MUQ would be relatively self-contained.

Another note: the final SIAM JUQ version of the Parno/Marzouk paper has a few minor fixes that are not in the arXiv version. So have a look at that one too.

best, youssef

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Hi youssef,

Thanks for your advice. I will have a look at that one too.

Looking forward to monotone transport parameterizations of map-accelerated MCMC algorithm.

Best,

Aaron