Simulation of forward-reverse stochastic representations for conditional diffusions

Bayer, Christian; Schoenmakers, John

doi:10.1214/13-aap969

Cited by 11 publications

(40 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The simulation of diffusion bridges has received much attention over the past decade, see for instance the papers Elerian et al [11], Eraker [12], Roberts and Stramer [21], Durham and Gallant [10], Stuart et al [22], Beskos and Roberts [5], Beskos et al [3], Beskos et al [4], Fearnhead [13], Papaspiliopoulos and Roberts [20], Lin et al [17], Bladt and Sørensen [6], Bayer and Schoenmakers [2] to mention just a few. Many of these papers employ accept-reject-type methods.…”

Section: Diffusion Bridgesmentioning

confidence: 99%

Guided proposals for simulating multi-dimensional diffusion bridges

Schauer¹,

Meulen²,

Zanten³

2017

Bernoulli

131

View full text Add to dashboard Cite

A Monte Carlo method for simulating a multi-dimensional diffusion process conditioned on hitting a fixed point at a fixed future time is developed. Proposals for such diffusion bridges are obtained by superimposing an additional guiding term to the drift of the process under consideration. The guiding term is derived via approximation of the target process by a simpler diffusion processes with known transition densities. Acceptance of a proposal can be determined by computing the likelihood ratio between the proposal and the target bridge, which is derived in closed form. We show under general conditions that the likelihood ratio is well defined and show that a class of proposals with guiding term obtained from linear approximations fall under these conditions.

show abstract

Section: Diffusion Bridgesmentioning

confidence: 99%

Guided proposals for simulating multi-dimensional diffusion bridges

Schauer¹,

Meulen²,

Zanten³

2017

Bernoulli

131

View full text Add to dashboard Cite

show abstract

“…Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php 399 Similar observations can be made for diffusion processes, where the lattice is approximated by a continuum of states and the Poissonian noise is replaced by Gaussian noise. Sampling bridges from diffusions is still an ongoing research area; see [1] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Multiscale Modeling of Wear Degradation in Cylinder Liners

Moraes

Ruggeri

Tempone

et al. 2014

Multiscale Model. Simul.

View full text Add to dashboard Cite

Abstract. Every mechanical system is naturally subjected to some kind of wear process that, at some point, will cause failure in the system if no monitoring or treatment process is applied. Since failures often lead to high economical costs, it is essential both to predict and to avoid them. To achieve this, a monitoring system of the wear level should be implemented to decrease the risk of failure. In this work, we take a first step into the development of a multiscale indirect inference methodology for state-dependent Markovian pure jump processes. This allows us to model the evolution of the wear level and to identify when the system reaches some critical level that triggers a maintenance response. Since the likelihood function of a discretely observed pure jump process does not have an expression that is simple enough for standard nonsampling optimization methods, we approximate this likelihood by expressions from upscaled models of the data. We use the Master Equation (ME) to assess the goodness-of-fit and to compute the distribution of the hitting time to the critical level.

show abstract

“…For a literature review on computational algorithms for computing conditional expectations of functionals of diffusion processes we refer to [3].…”

Section: Bridge Simulation For Sdesmentioning

confidence: 99%

“…Moreover, we assume that p(s, x, t, y) > 0. Once again, the fundamental idea of the forward-reverse algorithm of Bayer and Schoenmakers [3] is to simulate trajectories of X (f ) and (independently) of X (b) and then look for any pairs that are "linked". Since the state space is now discrete, we may, in principle, require exact linkage in the sense that we may only consider pairs such that X (f ) (t * ) = X (b) (t * ).…”

Section: The Forward-reverse Formula For Srn Let Us Consider a Time mentioning

confidence: 99%

“…The "missing data" can be gathered by simulating SRN bridges of the process X conditional on D, i.e., X(s k )=x(s k ) and X(t k )=x(t k ) for all intervals [s k , t k ]. To simulate SRN bridges, we extend the forward-reverse technique developed by Bayer and Schoenmakers [3] for Itô diffusions to the case of SRNs. As explained in Section 2, the forward-reverse algorithm generates forward paths from s k to t * k and backward paths from t k to t * k .…”

mentioning

confidence: 99%

See 1 more Smart Citation

An efficient forward–reverse expectation-maximization algorithm for statistical inference in stochastic reaction networks

Bayer

Moraes

Tempone

et al. 2016

Stochastic Analysis and Applications

Self Cite

View full text Add to dashboard Cite

Abstract. In this work, we present an extension to the context of Stochastic Reaction Networks (SRNs) of the forward-reverse representation introduced in "Simulation of forward-reverse stochastic representations for conditional diffusions", a 2014 paper by Bayer and Schoenmakers. We apply this stochastic representation in the computation of efficient approximations of expected values of functionals of SNR bridges, i.e., SRNs conditioned to its values in the extremes of given time-intervals. We then employ this SNR bridge-generation technique to the statistical inference problem of approximating the reaction propensities based on discretely observed data. To this end, we introduce a two-phase iterative inference method in which, during phase I, we solve a set of deterministic optimization problems where the SRNs are replaced by their reaction-rate Ordinary Differential Equations (ODEs) approximation; then, during phase II, we apply the Monte Carlo version of the Expectation-Maximization (EM) algorithm starting from the phase I output. By selecting a set of over dispersed seeds as initial points for phase I, the output of parallel runs from our two-phase method is a cluster of approximate maximum likelihood estimates. Our results are illustrated by numerical examples.

show abstract

Simulation of forward-reverse stochastic representations for conditional diffusions

Cited by 11 publications

References 21 publications

Guided proposals for simulating multi-dimensional diffusion bridges

Guided proposals for simulating multi-dimensional diffusion bridges

Multiscale Modeling of Wear Degradation in Cylinder Liners

An efficient forward–reverse expectation-maximization algorithm for statistical inference in stochastic reaction networks

Contact Info

Product

Resources

About