A Variance-Reduced Multilevel Monte Carlo Algorithm for Maximum Likelihood Inference in Multivariate Diffusions
(2018) 12th International Workshop on Rare-Event Simulation- Abstract
- We introduce a Multilevel Monte Carlo method for approximating the transition
density for discretely observed multivariate diffusion processes. These are
used within a Pseudo-marginal Metropolis-Hastings (PMMH) algorithm to do Bayesian
inference on the parameters.
The Pedersen representation shows how the transition density can be represented
as a conditional expectation, but the corresponding Monte Carlo algorithm
can be quite costly. Multilevel Monte Carlo is a recent, popular method for reducing
the computational cost for approximations of conditional expectations. These
ideas are combined in the paper.
Both theoretical comparisons and simulations show that the proposed multilevel
method is able... (More) - We introduce a Multilevel Monte Carlo method for approximating the transition
density for discretely observed multivariate diffusion processes. These are
used within a Pseudo-marginal Metropolis-Hastings (PMMH) algorithm to do Bayesian
inference on the parameters.
The Pedersen representation shows how the transition density can be represented
as a conditional expectation, but the corresponding Monte Carlo algorithm
can be quite costly. Multilevel Monte Carlo is a recent, popular method for reducing
the computational cost for approximations of conditional expectations. These
ideas are combined in the paper.
Both theoretical comparisons and simulations show that the proposed multilevel
method is able to reduce the variance of the estimates substantially, when
keeping the bias and computational cost fixed relative to the standard Monte Carlo
approximations. Lower variance leads to better mixing in the PMMH algorithm,
which is confirmed in a simulation study using Bayesian inference. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/7c167a37-a3ae-4b8d-b194-21c955a680d7
- author
- Lindström, Erik LU and Åkerlindh, Carl LU
- organization
- publishing date
- 2018-08-31
- type
- Contribution to conference
- publication status
- published
- conference name
- 12th International Workshop on Rare-Event Simulation
- conference location
- Stockholm, Sweden
- conference dates
- 2018-08-29 - 2018-08-31
- language
- English
- LU publication?
- yes
- id
- 7c167a37-a3ae-4b8d-b194-21c955a680d7
- date added to LUP
- 2019-02-27 09:18:55
- date last changed
- 2021-03-22 21:30:32
@misc{7c167a37-a3ae-4b8d-b194-21c955a680d7, abstract = {{We introduce a Multilevel Monte Carlo method for approximating the transition<br/>density for discretely observed multivariate diffusion processes. These are<br/>used within a Pseudo-marginal Metropolis-Hastings (PMMH) algorithm to do Bayesian<br/>inference on the parameters.<br/>The Pedersen representation shows how the transition density can be represented<br/>as a conditional expectation, but the corresponding Monte Carlo algorithm<br/>can be quite costly. Multilevel Monte Carlo is a recent, popular method for reducing<br/>the computational cost for approximations of conditional expectations. These<br/>ideas are combined in the paper.<br/>Both theoretical comparisons and simulations show that the proposed multilevel<br/>method is able to reduce the variance of the estimates substantially, when<br/>keeping the bias and computational cost fixed relative to the standard Monte Carlo<br/>approximations. Lower variance leads to better mixing in the PMMH algorithm,<br/>which is confirmed in a simulation study using Bayesian inference.}}, author = {{Lindström, Erik and Åkerlindh, Carl}}, language = {{eng}}, month = {{08}}, title = {{A Variance-Reduced Multilevel Monte Carlo Algorithm for Maximum Likelihood Inference in Multivariate Diffusions}}, year = {{2018}}, }