Almanac: HMC sampling with bounded velocity

arXiv (Cornell University)

Abstract

In Hamiltonian Monte Carlo sampling, the shape of the potential and the choice of the momentum distribution jointly give rise to the Hamiltonian dynamics of the sampler. An efficient sampler propagates quickly in all regions of the parameter space, so that the chain has a low autocorrelation length and the sampler has a high acceptance rate, with the goal of optimising the number of near-independent samples for given computational cost. Standard Gaussian momentum distributions allow arbitrarily large velocities, which can lead to inefficient exploration in posteriors with ridges or funnel-like geometries. We investigate alternative momentum distributions based on relativistic and Student's t kinetic energies, which naturally limit particle velocities and may improve robustness. Using Almanac, a sampler for cosmological posterior distributions of sky maps and power spectra on the sphere, we test these alternatives in both low- and high-dimensional settings. We find that the choice of parameterization and momentum distribution can improve convergence and effective sample rate, though the achievable gains are generally modest and strongly problem-dependent, reaching up to an order of magnitude in favorable cases. Among the momentum distributions that we tested, those with moderately heavy tails achieved the best balance between efficiency and stability. These results highlight the importance of sampler design and encourage future work on adaptive and self-tuning strategies for kinetic energy parameter optimization in high-dimensional settings.

Authors 7

1. Javier Silva Lafaurie Aachen Leiden Observatory Mathematical Institute

   Leiden University

   Affiliation as printed

   Leiden Observatory , Leiden University , Gorlaeus Gebouw , Einsteinweg 55 , NL-2333 CC Leiden , The Netherlands

   Mathematical Institute , Leiden University , Gorlaeus Gebouw , Einsteinweg 55 , NL-2333 CC Leiden , The Netherlands

2. L Whiteway

   University College London

   Affiliation as printed

   Department of Physics and Astronomy , University College London , Gower Street , London WC1E 6BT , UK

3. Elena Sellentin Aachen Leiden Observatory Mathematical Institute

   Leiden University

   Affiliation as printed

   Leiden Observatory , Leiden University , Gorlaeus Gebouw , Einsteinweg 55 , NL-2333 CC Leiden , The Netherlands

   Mathematical Institute , Leiden University , Gorlaeus Gebouw , Einsteinweg 55 , NL-2333 CC Leiden , The Netherlands

4. Kutay Nazli Aachen Leiden Observatory Mathematical Institute

   Leiden University

   Affiliation as printed

   Leiden Observatory , Leiden University , Gorlaeus Gebouw , Einsteinweg 55 , NL-2333 CC Leiden , The Netherlands

   Mathematical Institute , Leiden University , Gorlaeus Gebouw , Einsteinweg 55 , NL-2333 CC Leiden , The Netherlands

5. Andrew H. Jaffe

   Imperial College London

   Affiliation as printed

   Astrophysics Group and Imperial Centre for Inference and Cosmology (ICIC) , Blackett Laboratory , Imperial College London , Prince Consort Road , London SW7 2AZ , UK and

6. Alan F. Heavens

   Imperial College London

   Affiliation as printed

   Astrophysics Group and Imperial Centre for Inference and Cosmology (ICIC) , Blackett Laboratory , Imperial College London , Prince Consort Road , London SW7 2AZ , UK and

7. Arthur Loureiro

   Stockholm University · AlbaNova · Imperial College London

   Affiliation as printed

   Astrophysics Group and Imperial Centre for Inference and Cosmology (ICIC) , Blackett Laboratory , Imperial College London , Prince Consort Road , London SW7 2AZ , UK and

   The Oskar Klein Centre , Department of Physics , Stockholm University , AlbaNova University Centre , SE-106 91 Stockholm , Sweden