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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - The Apogee to Apogee Path Sampler
AU - Sherlock, Chris
AU - Urbas, Szymon
AU - Ludkin, Matthew
PY - 2023/10/2
Y1 - 2023/10/2
N2 - Among 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 initialize the integration. We present the Apogee to Apogee Path Sampler (AAPS), which uses 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. Supplementary materials for this article are available online.
AB - Among 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 initialize the integration. We present the Apogee to Apogee Path Sampler (AAPS), which uses 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. Supplementary materials for this article are available online.
KW - Hamiltonian Monte Carlo
KW - Leapfrog step
KW - Markov chain Monte Carlo
KW - Robustness to tuning
U2 - 10.1080/10618600.2023.2190784
DO - 10.1080/10618600.2023.2190784
M3 - Journal article
VL - 32
SP - 1436
EP - 1446
JO - Journal of Computational and Graphical Statistics
JF - Journal of Computational and Graphical Statistics
SN - 1061-8600
IS - 4
ER -