On the exact and $\varepsilon$-strong simulation of (jump) diffusions

Pollock, Murray; Johansen, Adam M.; Roberts, Gareth O.

doi:10.3150/14-bej676

Cited by 41 publications

(57 citation statements)

References 41 publications

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“…(), Pollock () and Pollock et al . ()), in which (in the simplest setting) the latent process is a diffusion satisfying the stochastic differential equation

d X_{t} = α false(X_{t} false) d t + d B_{t}, X_{0} = x, t \in false[0, T false] .

…”

Section: Discussion On the Paper By Gerber And Chopinmentioning

confidence: 99%

Sequential Quasi Monte Carlo

Gerber

Chopin

2015

Journal of the Royal Statistical Society Series B: Statistical Methodology

118

135

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Summary. We derive and study sequential quasi Monte Carlo (SQMC), a class of algorithms obtained by introducing QMC point sets in particle filtering. SQMC is related to, and may be seen as an extension of, the array-RQMC algorithm of L'Ecuyer and his colleagues. The complexity of SQMC is O{N log.N/}, where N is the number of simulations at each iteration, and its error rate is smaller than the Monte Carlo rate O P .N 1=2 /. The only requirement to implement SQMC algorithms is the ability to write the simulation of particle x n t given x n t 1 as a deterministic function of x n t 1 and a fixed number of uniform variates. We show that SQMC is amenable to the same extensions as standard SMC, such as forward smoothing, backward smoothing and unbiased likelihood evaluation. In particular, SQMC may replace SMC within a particle Markov chain Monte Carlo algorithm. We establish several convergence results. We provide numerical evidence that SQMC may significantly outperform SMC in practical scenarios.

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“…(), Pollock () and Pollock et al . ()), in which (in the simplest setting) the latent process is a diffusion satisfying the stochastic differential equation

d X_{t} = α false(X_{t} false) d t + d B_{t}, X_{0} = x, t \in false[0, T false] .

…”

Section: Discussion On the Paper By Gerber And Chopinmentioning

confidence: 99%

Sequential Quasi Monte Carlo

Gerber

Chopin

2015

Journal of the Royal Statistical Society Series B: Statistical Methodology

118

135

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show abstract

“…, Ξ K is a research topic in its own right, as it involves simulating a stopped diffusion process. We do not discuss this further, rather we refer the reader to literature on this topic; see for instance Beskos et al (2006) and Pollock et al (2013). The velocity field v 2 (s) in (26) is defined as the weighted average of the values of v H 2 (·) at the grid locations closest to s. The velocity field v 1 (s)…”

Section: Application: Estimating Ocean Circulationmentioning

confidence: 99%

A Monte Carlo approach to quantifying model error in Bayesian parameter estimation

White

Herbei

2015

Computational Statistics & Data Analysis

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“…Overview of the exact algorithm. Here we give a brief overview of the exact algorithm (EA) of Beskos and Roberts (2005), Roberts (2006, 2008), and Pollock, Johansen and Roberts (2016), and we refer the reader to those papers for further details. The EA returns a recipe for simulating the sample paths of a diffusion X = (X t ) t∈[0,T ] satisfying the sde…”

Section: 1mentioning

confidence: 99%

Exact simulation of the Wright–Fisher diffusion

Jenkins¹,

Spanò²

2017

Ann. Appl. Probab.

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The Wright-Fisher family of diffusion processes is a widely used class of evolutionary models. However, simulation is difficult because there is no known closed-form formula for its transition function. In this article we demonstrate that it is in fact possible to simulate exactly from a broad class of Wright-Fisher diffusion processes and their bridges. For those diffusions corresponding to reversible, neutral evolution, our key idea is to exploit an eigenfunction expansion of the transition function; this approach even applies to its infinitedimensional analogue, the Fleming-Viot process. We then develop an exact rejection algorithm for processes with more general drift functions, including those modelling natural selection, using ideas from retrospective simulation. Our approach also yields methods for exact simulation of the moment dual of the Wright-Fisher diffusion, the ancestral process of an infinite-leaf Kingman coalescent tree. We believe our new perspective on diffusion simulation holds promise for other models admitting a transition eigenfunction expansion. * Supported in part by EPSRC Research Grant EP/L018497/1. MSC 2010 subject classifications: Primary 65C05; secondary 60H35, 60J60, 92D15

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On the exact and $\varepsilon$-strong simulation of (jump) diffusions

Cited by 41 publications

References 41 publications

Sequential Quasi Monte Carlo

Sequential Quasi Monte Carlo

A Monte Carlo approach to quantifying model error in Bayesian parameter estimation

Exact simulation of the Wright–Fisher diffusion

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