Livingstone, S;
Betancourt, M;
Byrne, S;
Girolami, M;
(2019)
On the Geometric Ergodicity of Hamiltonian Monte Carlo.
Bernoulli
, 25
(4A)
pp. 3109-3138.
10.3150/18-BEJ1083.
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Abstract
We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic. We consider implementations with both position-independent and position-dependent integration times. In the former case we find that the conditions for geometric ergodicity are essentially a gradient of the log-density which asymptotically points towards the centre of the space and grows no faster than linearly. In an idealised scenario in which the integration time is allowed to change in different regions of the space, we show that geometric ergodicity can be recovered for a much broader class of tail behaviours, leading to some guidelines for the choice of this free parameter in practice.
| Type: | Article |
|---|---|
| Title: | On the Geometric Ergodicity of Hamiltonian Monte Carlo |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.3150/18-BEJ1083 |
| Publisher version: | https://doi.org/10.3150/18-BEJ1083 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10060213 |
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