Particle Methods for Stochastic Differential Equation Mixed Effects Models

Botha, Imke; Kohn, Robert; Drovandi, Christopher

doi:10.1214/20-ba1216

Cited by 18 publications

(16 citation statements)

References 41 publications

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“…The key research problem in this study is the latest developments of accurate and computationally optimal parameter-estimation procedures based on the approximated maximum-likelihood technique, which cannot be implemented in the presence of a closedform expression for the mixed-effect parameters SDE [21]. Our developed maximumlikelihood estimation technique relies on the fact that the conditional bivariate probability density function has an exact form.…”

Section: Parameter-estimating Resultsmentioning

confidence: 99%

Symmetric and Asymmetric Diffusions through Age-Varying Mixed-Species Stand Parameters

Rupšys

Petrauskas

2021

Symmetry

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(1) Background: This paper deals with unevenly aged, whole-stand models from mixed-effect parameters diffusion processes and Voronoi diagram points of view and concentrates on the mixed-species stands in Lithuania. We focus on the Voronoi diagram of potentially available areas to tree positions as the measure of the competition effect of individual trees and the tree diameter at breast height to relate their evolution through time. (2) Methods: We consider a bivariate hybrid mixed-effect parameters stochastic differential equation for the parameterization of the diameter and available polygon area at age to ensure a proper description of the link between them during the age (time) span of a forest stand. In this study, the Voronoi diagram was used as a mathematical tool for the quantitative characterization of inter-tree competition. (3) Results: The newly derived model considers bivariate correlated observations, tree diameter, and polygon area arising from a particular stand and enables defining equations for calculating diameter, polygon-area, and stand-density predictions and forecasts. (4) Conclusions: From a statistical point of view, the newly developed models produced acceptable statistical measures of predictions and forecasts. All the results were implemented in the Maple computer algebra system.

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Section: Parameter-estimating Resultsmentioning

confidence: 99%

Symmetric and Asymmetric Diffusions through Age-Varying Mixed-Species Stand Parameters

Rupšys

Petrauskas

2021

Symmetry

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“…In fact, while the variability of these estimates can be mitigated by increasing the number of particles, of course this has negative consequences on the computational budget. Instead CPM strategies allow for considerably smaller number of particles when trying to alleviate the stickiness problem, see for example Golightly et al (2019) for applications to stochastic kinetic models, and Wiqvist et al (2021) and Botha et al (2021) for stochastic differential equation mixed-effects models. Interestingly, implementing CPM approaches is trivial.…”

Section: Correlated Synthetic Likelihoodmentioning

confidence: 99%

Sequentially Guided MCMC Proposals for Synthetic Likelihoods and Correlated Synthetic Likelihoods

2023

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Synthetic likelihood (SL) is a strategy for parameter inference when the likelihood function is analytically or computationally intractable. In SL, the likelihood function of the data is replaced by a multivariate Gaussian density over summary statistics of the data. SL requires simulation of many replicate datasets at every parameter value considered by a sampling algorithm, such as Markov chain Monte Carlo (MCMC), making the method computationally-intensive. We propose two strategies to alleviate the computational burden. First, we introduce an algorithm producing a proposal distribution that is sequentially tuned and made conditional to data, thus it rapidly guides the proposed parameters towards high posterior density regions. In our experiments, a small number of iterations of our algorithm is enough to rapidly locate high density regions, which we use to initialize one or several chains that make use of off-the-shelf adaptive MCMC methods. Our "guided" approach can also be potentially used with MCMC samplers for approximate Bayesian computation (ABC). Second, we exploit strategies borrowed from the correlated pseudo-marginal MCMC literature, to improve the chains mixing in a SL framework. Moreover, our methods enable inference for challenging case studies, when the posterior is multimodal and when the chain is initialised in low posterior probability regions of the parameter space, where standard samplers failed. To illustrate the advantages stemming from our framework we consider five benchmark examples, including estimation of parameters for a cosmological model and a stochastic model with highly non-Gaussian summary statistics.

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“…MCMC can be applied to detect identifiability for any stochastic model provided an approximation to the likelihood is available. Recent developments to particle MCMC have seen its adoption for more complicated SDE models, such as SDE mixed effects models [173]. For systems with relatively small populations, it may be more appropriate to work directly with an SSA with, for example, a tau-leap method [57,125].…”

Section: Particle Markov Chain Monte Carlomentioning

confidence: 99%

Identifiability analysis for stochastic differential equation models in systems biology

Browning

Warne

Burrage

et al. 2020

J. R. Soc. Interface.

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Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability , we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically motivated synthetic data and Markov chain Monte Carlo methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github .

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Particle Methods for Stochastic Differential Equation Mixed Effects Models

Cited by 18 publications

References 41 publications

Symmetric and Asymmetric Diffusions through Age-Varying Mixed-Species Stand Parameters

Symmetric and Asymmetric Diffusions through Age-Varying Mixed-Species Stand Parameters

Sequentially Guided MCMC Proposals for Synthetic Likelihoods and Correlated Synthetic Likelihoods

Identifiability analysis for stochastic differential equation models in systems biology

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