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 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.
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.
| Original language | English |
|---|---|
| Publication status | Published - 2018 Aug 31 |
| Event | 12th International Workshop on Rare-Event Simulation - KTH Royal Institute of Technology, Stockholm, Sweden Duration: 2018 Aug 29 → 2018 Aug 31 Conference number: 18 https://people.kth.se/~pierren/resim2018/resim2018.html |
Conference
| Conference | 12th International Workshop on Rare-Event Simulation |
|---|---|
| Abbreviated title | RESIM |
| Country/Territory | Sweden |
| City | Stockholm |
| Period | 2018/08/29 → 2018/08/31 |
| Internet address |