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A Variance-Reduced Multilevel Monte Carlo Algorithm for Maximum Likelihood Inference in Multivariate Diffusions

Lindström, Erik LU and Åkerlindh, Carl LU (2018) 12th International Workshop on Rare-Event Simulation
Abstract (Swedish)
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)
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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
2019-05-25 02:17:33
@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},
}