Taking error into account when fitting models using Approximate Bayesian Computation

Vaart, Elske van der; Prangle, Dennis; Sibly, Richard M.

doi:10.1002/eap.1656

Cited by 10 publications

(13 citation statements)

References 32 publications

(61 reference statements)

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“…Our results suggest that while most of the uncertainty about the future stems from different potential scenarios of habitat loss, there is significant uncertainty stemming from unknown parameters in the IBM. The latter will hopefully reduce as improved methods are developed in data assimilation (see, e.g., van der Vaart, Prangle, & Sibly, 2018).…”

Section: Discussionmentioning

confidence: 99%

Human‐driven habitat conversion is a more immediate threat to Amboseli elephants than climate change

Boult

Fishlock

Quaife

et al. 2019

Conservat Sci and Prac

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Global ecosystem change presents a major challenge to biodiversity conservation, which must identify and prioritize the most critical threats to species persistence given limited available funding. Mechanistic models enable robust predictions under future conditions and can consider multiple stressors in combination. Here we use an individual-based model (IBM) to predict elephant population size in Amboseli, southern Kenya, under environmental scenarios incorporating climate change and anthropogenic habitat loss. The IBM uses projected food availability as a key driver of elephant population dynamics and relates variation in food availability to changes in vital demographic rates through an energy budget. Habitat loss, rather than climate change, represents the most significant threat to the persistence of the Amboseli elephant population in the 21st century and highlights the importance of collaborations and agreements that preserve space for Amboseli elephants to ensure the population remains resilient to environmental stochasticity. K E Y W O R D Sclimate change, conservation planning, elephants, habitat loss, individual-based model

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Section: Discussionmentioning

confidence: 99%

Human‐driven habitat conversion is a more immediate threat to Amboseli elephants than climate change

Boult

Fishlock

Quaife

et al. 2019

Conservat Sci and Prac

Self Cite

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“…This leads to a longer computational time, which is prohibitive for the case of ODE model parameter inference. The total CPU time when we applied the Vaart et al [34] algorithm to the first test problem to have 1000 samples is 29 h which was derived from 2 × 10 6 simulations and this time is much larger than when we used the MCMC method for this example (5.25 min).…”

Section: Including the Error Term In The Abc Algorithmmentioning

confidence: 93%

“…Here we have used the coordinates of z and y directly, following the approach of Toni et al [16] for inference of ODE model parameters. Vaart et al [34] proposed an ABC method called error-calibrated ABC that implements a general methodology introduced by Wilkinson [35]. In their method, they incorporated the estimation of the noise into the ABC technique by identifying an ABC acceptance probability in which the noise is assumed to be normally distributed and independent.…”

Section: Bayesian Techniques For Ode Parameter Inferencementioning

confidence: 99%

“…Including the error term in the ABC algorithm may overcome this limitation and work inspired by Wilkinson [35] in Vaart et al [34], as has been explained in §2, argued that the acceptance of the proposed parameters should be with respect to the error term rather than with respect to some tolerance level. In their method they assumed that the error term follows a normal distribution.…”

Section: Including the Error Term In The Abc Algorithmmentioning

confidence: 99%

“…As a consequence, applying MCMC ABC was difficult because this lack of information makes the choice of an appropriate e problematic. In this paper, in order to select an appropriate tolerance level we adopted the method of Vaart et al [34], which is to solve the ODE model with different proposals of the parameters from the priors, find all the distances using 3.2 between these solutions and the true data, and then choose the one that minimizes this distance. We then used the best fitting solution to estimate the value of the MCMC ABC tolerance which was e = 116230.8.…”

Section: Application: Malaria In Afghanistanmentioning

confidence: 99%

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A comparison of approximate versus exact techniques for Bayesian parameter inference in nonlinear ordinary differential equation models

et al. 2020

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The behaviour of many processes in science and engineering can be accurately described by dynamical system models consisting of a set of ordinary differential equations (ODEs). Often these models have several unknown parameters that are difficult to estimate from experimental data, in which case Bayesian inference can be a useful tool. In principle, exact Bayesian inference using Markov chain Monte Carlo (MCMC) techniques is possible; however, in practice, such methods may suffer from slow convergence and poor mixing. To address this problem, several approaches based on approximate Bayesian computation (ABC) have been introduced, including Markov chain Monte Carlo ABC (MCMC ABC) and sequential Monte Carlo ABC (SMC ABC). While the system of ODEs describes the underlying process that generates the data, the observed measurements invariably include errors. In this paper, we argue that several popular ABC approaches fail to adequately model these errors because the acceptance probability depends on the choice of the discrepancy function and the tolerance without any consideration of the error term. We observe that the so-called posterior distributions derived from such methods do not accurately reflect the epistemic uncertainties in parameter values. Moreover, we demonstrate that these methods provide minimal computational advantages over exact Bayesian methods when applied to two ODE epidemiological models with simulated data and one with real data concerning malaria transmission in Afghanistan.

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Integrating an individual-based model with approximate Bayesian computation to predict the invasion of a freshwater fish provides insights into dispersal and range expansion dynamics

et al. 2020

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Short-distance dispersal enables introduced alien species to colonise and invade local habitats following their initial introduction, but is often poorly understood for many freshwater taxa. Knowledge gaps in range expansion of alien species can be overcome using predictive approaches such as individual based models (IBMs), especially if predictions can be improved through fitting to empirical data, but this can be challenging for models having multiple parameters. We therefore estimated the parameters of a model implemented in the RangeShifter IBM platform by approximate Bayesian computation (ABC) in order to predict the further invasion of a lowland river (Great Ouse, England) by a small-bodied invasive fish (bitterling Rhodeus sericeus). Prior estimates for parameters were obtained from the literature and expert opinion. Model fitting was conducted using a time-series (1983 to 2018) of sampling data at fixed locations and revealed that for 5 of 11 model parameters, the posterior distributions differed markedly from prior assumptions. In particular, sub-adult maximum emigration probability was substantially higher in the posteriors than priors. Simulations of bitterling range expansion predicted that following detection in 1984, their early expansion involved a relatively high population growth rate that stabilised after 5 years. The pattern of bitterling patch occupancy was sigmoidal, with 20% of the catchment occupied after 20 years, increasing to 80% after 30 years. Predictions were then for 95% occupancy after 69 years. The development of this IBM thus successfully simulated the range expansion dynamics of this small-bodied invasive fish, with ABC improving the simulation precision. This combined methodology also highlighted that sub-adult dispersal was more likely to contribute to the rapid colonisation rate than expert opinion suggested. These results emphasise the importance of time-series data for refining IBM parameters generally and increasing our understanding of dispersal behaviour and range expansion dynamics specifically. Keywords Biological invasion Á Bitterling Á Leading edge dispersal Á RangeShifter Á River catchment Á Simulation model

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Taking error into account when fitting models using Approximate Bayesian Computation

Cited by 10 publications

References 32 publications

Human‐driven habitat conversion is a more immediate threat to Amboseli elephants than climate change

Human‐driven habitat conversion is a more immediate threat to Amboseli elephants than climate change

A comparison of approximate versus exact techniques for Bayesian parameter inference in nonlinear ordinary differential equation models

Integrating an individual-based model with approximate Bayesian computation to predict the invasion of a freshwater fish provides insights into dispersal and range expansion dynamics

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