The Apogee to Apogee Path Sampler

Sherlock, Chris and Urbas, Szymon and Ludkin, Matthew (2023) The Apogee to Apogee Path Sampler. Journal of Computational and Graphical Statistics. ISSN 1061-8600

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Amongst Markov chain Monte Carlo algorithms, Hamiltonian Monte Carlo (HMC) is often the algorithm of choice for complex, high-dimensional target distributions; however, its efficiency is notoriously sensitive to the choice of the integration-time tuning parameter. When integrating both forward and backward in time using the same leapfrog integration step as HMC, the set of apogees, local maxima in the potential along a path, is the same whatever point (position and momentum) along the path is chosen to initialise the integration. We present the Apogee to Apogee Path Sampler (AAPS), which utilises this invariance to create a simple yet generic methodology for constructing a path, proposing a point from it and accepting or rejecting that proposal so as to target the intended distribution. We demonstrate empirically that AAPS has a similar efficiency to HMC but is much more robust to the setting of its equivalent tuning parameter, the number of apogees that the path crosses.

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Journal Article
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Journal of Computational and Graphical Statistics
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22 Mar 2023 10:05
Last Modified:
17 Sep 2023 03:25