Bayesian inference for stochastic differential equation mixed effects models

Botha, Imke

doi:10.5204/thesis.eprints.198039

Cited by 2 publications

(2 citation statements)

References 36 publications

(55 reference statements)

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“…For practical illustrative purposes, we focus on the fundamental method of particle marginal Metropolis-Hastings (Andrieu et al, 2010) using the bootstrap particle filter (Gordon et al, 1993) for likelihood estimation. There are many other variants to this classic approach, such as particle Gibbs sampling (Andrieu et al, 2010;Doucet et al, 2015), coupled Markov chains (Dodwell et al, 2015(Dodwell et al, , 2019, and more advanced particle filters (Doucet and Johanson, 2011) and proposal mechanisms (Botha et al, 2019;Cotter et al, 2013). It is also important to note that the pseudo-marginal approach is equally valid for Bayesian sampling strategies based on sequential Monte Carlo (Del Moral et al, 2006;Li et al, 2019;Sisson et al, 2007).…”

Section: Discussionmentioning

confidence: 99%

A practical guide to pseudo-marginal methods for computational inference in systems biology

Warne

Baker

Simpson

2020

Journal of Theoretical Biology

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For many stochastic models of interest in systems biology, such as those describing biochemical reaction networks, exact quantification of parameter uncertainty through statistical inference is intractable. Likelihood-free computational inference techniques enable parameter inference when the likelihood function for the model is intractable but the generation of many sample paths is feasible through stochastic simulation of the forward problem. The most common likelihood-free method in systems biology is approximate Bayesian computation that accepts parameters that result in low discrepancy between stochastic simulations and measured data. However, it can be difficult to assess how the accuracy of the resulting inferences are affected by the choice of acceptance threshold and discrepancy function. The pseudo-marginal approach is an alternative likelihood-free inference method that utilises a Monte Carlo estimate of the likelihood function. This approach has several advantages, particularly in the context of noisy, partially observed, time-course data typical in biochemical reaction network studies. Specifically, the pseudo-marginal approach facilitates exact inference and uncertainty quantification, and may be efficiently combined with particle filters for low variance, high-accuracy likelihood estimation. In this review, we provide a practical introduction to the pseudo-marginal approach using inference for biochemical reaction networks as a series of case studies. Implementations of key algorithms and examples are provided using the Julia programming language; a high performance, open source programming language for scientific computing (https://github.com/davidwarne/Warne2019 GuideToPseudoMarginal).

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Section: Discussionmentioning

confidence: 99%

A practical guide to pseudo-marginal methods for computational inference in systems biology

Warne

Baker

Simpson

2020

Journal of Theoretical Biology

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“…A comparison of aCPMMH with approaches that target the joint posterior of the parameters and latent process also warrants further attention; see e.g. Botha (2020) for an implementation of the latter.…”

Section: Limitations and Future Directionsmentioning

confidence: 99%

Augmented pseudo-marginal Metropolis–Hastings for partially observed diffusion processes

Golightly

Sherlock

2022

Stat Comput

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We consider the problem of inference for nonlinear, multivariate diffusion processes, satisfying Itô stochastic differential equations (SDEs), using data at discrete times that may be incomplete and subject to measurement error. Our starting point is a state-of-the-art correlated pseudo-marginal Metropolis–Hastings algorithm, that uses correlated particle filters to induce strong and positive correlation between successive likelihood estimates. However, unless the measurement error or the dimension of the SDE is small, correlation can be eroded by the resampling steps in the particle filter. We therefore propose a novel augmentation scheme, that allows for conditioning on values of the latent process at the observation times, completely avoiding the need for resampling steps. We integrate over the uncertainty at the observation times with an additional Gibbs step. Connections between the resulting pseudo-marginal scheme and existing inference schemes for diffusion processes are made, giving a unified inference framework that encompasses Gibbs sampling and pseudo marginal schemes. The methodology is applied in three examples of increasing complexity. We find that our approach offers substantial increases in overall efficiency, compared to competing methods

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Bayesian inference for stochastic differential equation mixed effects models

Cited by 2 publications

References 36 publications

A practical guide to pseudo-marginal methods for computational inference in systems biology

A practical guide to pseudo-marginal methods for computational inference in systems biology

Augmented pseudo-marginal Metropolis–Hastings for partially observed diffusion processes

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