Bayesian Emulation and Calibration of a Stochastic Computer Model of Mitochondrial DNA Deletions in Substantia Nigra Neurons

Henderson, Daniel A.; Boys, Richard J.; Krishnan, Kim J.; Lawless, Conor; Wilkinson, Darren J.

doi:10.1198/jasa.2009.0005

Cited by 72 publications

(97 citation statements)

References 21 publications

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“…Any subsequent calculation one wishes to do with GALFORM can instead be performed far more efficiently using an emulator (Heitmann et al 2009). For example, an emulator can be used within an MCMC algorithm to greatly speed up convergence (Kennedy & O'Hagan 2001;Higdon et al 2004;Henderson et al 2009). This is especially useful as for scenarios possessing moderate to high numbers of input parameters, MCMC algorithms often require vast numbers (billions, trillions or more) of model evaluations to adequately explore the input space and reach convergence: see for example the excellent discussion in Geyer (2011).…”

Section: Bayesian Emulation Methodologymentioning

confidence: 99%

Constraints on galaxy formation models from the galaxy stellar mass function and its evolution

Rodrigues

Vernon

Bower

2016

Mon. Not. R. Astron. Soc.

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We explore the parameter space of the semi-analytic galaxy formation model GALFORM, studying the constraints imposed by measurements of the galaxy stellar mass function (GSMF) and its evolution. We use the Bayesian Emulator method to quickly eliminate vast implausible volumes of the parameter space and zoom in on the most interesting regions, allowing us to identify a set of models that match the observational data within model uncertainties. We find that the GSMF strongly constrains parameters related to quiescent star formation in discs, stellar and AGN feedback and threshold for disc instabilities, but weakly restricts other parameters. Constraining the model using local data alone does not usually select models that match the evolution of the GSMF well. Nevertheless, we show that a small subset of models provides acceptable match to GSMF data out to redshift 1.5. We explore the physical significance of the parameters of these models, in particular exploring whether the model provides a better description if the mass loading of the galactic winds generated by starbursts (β 0,burst ) and quiescent disks (β 0,disc ) is different. Performing a principal component analysis of the plausible volume of the parameter space, we write a set of relations between parameters obeyed by plausible models with respect to GSMF evolution. We find that while β 0,disc is strongly constrained by GSMF evolution data, constraints on β 0,burst are weak. Although it is possible to find plausible models for which β 0,burst = β 0,disc , most plausible models have β 0,burst > β 0,disc , implying -for these -larger SN feedback efficiency at higher redshifts.

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Section: Bayesian Emulation Methodologymentioning

confidence: 99%

Constraints on galaxy formation models from the galaxy stellar mass function and its evolution

Rodrigues

Vernon

Bower

2016

Mon. Not. R. Astron. Soc.

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“…Henderson et al [2009], Jandarov et al [2014, Wilkinson [2014], Meeds and Welling [2014] and Cameron et al [2015] each implement MCMC algorithms where the true likelihood is replaced by that derived from an emulator. Important differences between the methods lie in how the emulator is trained.…”

Section: Emulationmentioning

confidence: 99%

Approximate Bayesian Computation and Simulation-Based Inference for Complex Stochastic Epidemic Models

McKinley¹,

Vernon²,

Andrianakis³

et al. 2018

Statist. Sci.

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Abstract. Approximate Bayesian Computation (ABC) and other simulationbased inference methods are becoming increasingly used for inference in complex systems, due to their relative ease-of-implementation. We briefly review some of the more popular variants of ABC and their application in epidemiology, before using a real-world model of HIV transmission to illustrate some of challenges when applying ABC methods to high dimensional, computationally intensive models. We then discuss an alternative approach-history matching-that aims to address some of these issues, and conclude with a comparison between these different methodologies.

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“…The training set is defined as the pair D = {X, y}. A key property of GPs is that their posterior distribution, after taking into account the training data D, is still a GP; in this case, given a prior as in expression (27) and a training set D, we obtain a posterior GP process with updated mean and covariance functions. This allows us to make predictions.…”

Section: Gp Emulation General Frameworkmentioning

confidence: 99%

“…For each function, we test the emulator predictions against the observed values by using the LOO-CV method. To select the final covariance function for the GP emulator, we use the criterion that the predicted data will lie within the 95% CI in 95% of cases [27], i.e., we compute the percentage of points out of range for each emulator and then choose the model (covariance function) with the smallest number of cases outside the 95% CI. The 95% CIs are computed as in [45], i.e., by using the intervals (m j 2s j , m j + 2s j ) where m j and s j are respectively the predictive mean (32) and square root (standard deviation) of the variance (33) for a given design point⇠ j .…”

Section: Specification Of the Gp Emulation Modelmentioning

confidence: 99%

Gaussian process modelling for uncertainty quantification in convectively-enhanced dissolution processes in porous media

Crevillén-García

Wilkinson

Shah

et al. 2017

Advances in Water Resources

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(2017) Gaussian process modelling for uncertainty quantification in convectively-enhanced dissolution processes in porous media. Advances in Water Resources, 99 . pp. 1-14. Permanent WRAP URL:http://wrap.warwick.ac.uk/85680 Copyright and reuse:The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available.Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP url' above for details on accessing the published version and note that access may require a subscription. AbstractNumerical groundwater flow and dissolution models of physico-chemical processes in deep aquifers are usually subject to uncertainty in one or more of the model input parameters. This uncertainty is propagated through the equations and needs to be quantified and characterised in order to rely on the model outputs. In this paper we present a Gaussian process emulation method as a tool for performing uncertainty quantification in mathematical models for convection and dissolution processes in porous media. One of the advantages of this method is its ability to significantly reduce the computational cost of an uncertainty analysis, while yielding accurate results, compared to classical Monte Carlo methods. We apply the methodology to a model of convectively-enhanced dissolution processes occurring during carbon capture and storage. In this model, the Gaussian process methodology fails due to the presence of multiple branches of solutions emanating from a bifurcation point, i.e., two equilibrium states exist rather than one. To overcome this issue we use a classifier as a precursor to the Gaussian process emulation, after which we are able to successfully perform a full uncertainty analysis in the vicinity of the bifurcation point.

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Bayesian Emulation and Calibration of a Stochastic Computer Model of Mitochondrial DNA Deletions in Substantia Nigra Neurons

Cited by 72 publications

References 21 publications

Constraints on galaxy formation models from the galaxy stellar mass function and its evolution

Constraints on galaxy formation models from the galaxy stellar mass function and its evolution

Approximate Bayesian Computation and Simulation-Based Inference for Complex Stochastic Epidemic Models

Gaussian process modelling for uncertainty quantification in convectively-enhanced dissolution processes in porous media

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