Asymptotics of an Efficient Monte Carlo Estimation for the Transition Density of Diffusion Processes

Stramer, Osnat; Yan, Jun

doi:10.1007/s11009-006-9006-2

Cited by 18 publications

(16 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…No noticeable difference can be seen by choosing 200 or 1000 simulations to approximate the expectations in the EML algorithm. Stramer and Yan (2007a) suggest that in a related problem of Monte Carlo estimation for the transition densities of diffusions, the optimal number of simulations S is of the order M 2 , which in the two cases discussed here amounts to approximately 900 simulations. Note also that the EML procedure takes about a second to produce the optimal paramteter values for each of the data sets described in this subsection.…”

Section: Base Casesmentioning

confidence: 92%

Globally Optimal Parameter Estimates for Non-Linear Diffusions

Mijatović

Schneider

2008

SSRN Journal

View full text Add to dashboard Cite

This paper studies an approximation method for the log likelihood function of a non-linear diffusion process using the bridge of the diffusion. The main result (Theorem 1) shows that this approximation converges uniformly to the unknown likelihood function and can therefore be used efficiently with any algorithm for sampling from the law of the bridge. We also introduce an expected maximum likelihood (EML) algorithm for inferring the parameters of discretely observed diffusion processes. The approach is applicable to a subclass of non-linear SDEs with constant volatility and drift that is linear in the model parameters. In this setting globally optimal parameters are obtained in a single step by solving a square linear system whose dimension equals the number of parameters in the model. Simulation studies to test the EML algorithm show that it performs well when compared with algorithms based on the exact maximum likelihood as well as closed-form likelihood expansions.

show abstract

Section: Base Casesmentioning

confidence: 92%

Globally Optimal Parameter Estimates for Non-Linear Diffusions

Mijatović

Schneider

2008

SSRN Journal

View full text Add to dashboard Cite

show abstract

“…Here we notice that the Durham and Gallant proposal is robust to varying h, whereas the method of Pedersen performs poorly when h is small. This contrasting behaviour of the Pedersen and Durham and Gallant method can be shown to hold generally (see Stramer and Yan 2007b;Stramer and Yan 2007a;Delyon and Hu 2006).…”

Section: Importance Samplingmentioning

confidence: 95%

Computational methods for complex stochastic systems: a review of some alternatives to MCMC

Fearnhead

2007

Stat Comput

View full text Add to dashboard Cite

We consider analysis of complex stochastic models based upon partial information. MCMC and reversible jump MCMC are often the methods of choice for such problems, but in some situations they can be difficult to implement; and suffer from problems such as poor mixing, and the difficulty of diagnosing convergence. Here we review three alternatives to MCMC methods: importance sampling, the forward-backward algorithm, and sequential Monte Carlo (SMC). We discuss how to design good proposal densities for importance sampling, show some of the range of models for which the forward-backward algorithm can be applied, and show how resampling ideas from SMC can be used to improve the efficiency of the other two methods. We demonstrate these methods on a range of examples, including estimating the transition density of a diffusion and of a discrete-state continuous-time Markov chain; inferring structure in population genetics; and segmenting genetic divergence data.

show abstract

“…Use of (9) has been justified by Delyon and Hu (2006), who show that the distribution of the target process (conditional on x t j+1 ) is absolutely continuous with respect to the distribution of the solution to (9). We may therefore expect that a Metropolis-Hastings scheme that uses a proposal based on a discretisation of (9) will yield a non-zero acceptance rate as ∆τ → 0 (for a rigorous treatment of the limiting forms, we refer the reader to Delyon and Hu (2006), Stramer and Yan (2007) and to Papaspiliopoulos and Roberts (2012) for a recent discussion). However, it should also be noted that the linear drift function governing (9) is independent of the the drift function α(·) governing the target process.…”

Section: Modified Diffusion Bridgementioning

confidence: 99%

Bayesian Inference for Diffusion-Driven Mixed-Effects Models

Whitaker¹,

Golightly²,

Boys³

et al. 2017

Bayesian Anal.

View full text Add to dashboard Cite

Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units, SDE driven mixed-effects models allow the quantification of both between and within individual variation. Performing Bayesian inference for such models using discrete-time data that may be incomplete and subject to measurement error is a challenging problem and is the focus of this paper. We extend a recently proposed MCMC scheme to include the SDE driven mixed-effects framework. Fundamental to our approach is the development of a novel construct that allows for efficient sampling of conditioned SDEs that may exhibit nonlinear dynamics between observation times. We apply the resulting scheme to synthetic data generated from a simple SDE model of orange tree growth, and real data on aphid numbers recorded under a variety of different treatment regimes. In addition, we provide a systematic comparison of our approach with an inference scheme based on a tractable approximation of the SDE, that is, the linear noise approximation.

show abstract

Asymptotics of an Efficient Monte Carlo Estimation for the Transition Density of Diffusion Processes

Cited by 18 publications

References 14 publications

Globally Optimal Parameter Estimates for Non-Linear Diffusions

Globally Optimal Parameter Estimates for Non-Linear Diffusions

Computational methods for complex stochastic systems: a review of some alternatives to MCMC

Bayesian Inference for Diffusion-Driven Mixed-Effects Models

Contact Info

Product

Resources

About