Sequential Monte Carlo with Adaptive Weights for Approximate Bayesian Computation

Bonassi, Fernando V.; West, Mike

doi:10.1214/14-ba891

Cited by 51 publications

(60 citation statements)

References 33 publications

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“…We borrow the system biology 'toggle switch' model that was used in Bonassi et al (2011) and Bonassi and West (2015), inspired by studies of dynamic cellular networks. This provides an example where the design of specialized summaries can be replaced by the Wasserstein distance between empirical distributions.…”

Section: Toggle Switch Modelmentioning

confidence: 99%

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Approximate Bayesian Computation with the Wasserstein Distance

Bernton

Jacob

Gerber

et al. 2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

113

145

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Summary A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation has become a popular approach to overcome this issue, in which one simulates synthetic data sets given parameters and compares summaries of these data sets with the corresponding observed values. We propose to avoid the use of summaries and the ensuing loss of information by instead using the Wasserstein distance between the empirical distributions of the observed and synthetic data. This generalizes the well‐known approach of using order statistics within approximate Bayesian computation to arbitrary dimensions. We describe how recently developed approximations of the Wasserstein distance allow the method to scale to realistic data sizes, and we propose a new distance based on the Hilbert space filling curve. We provide a theoretical study of the method proposed, describing consistency as the threshold goes to 0 while the observations are kept fixed, and concentration properties as the number of observations grows. Various extensions to time series data are discussed. The approach is illustrated on various examples, including univariate and multivariate g‐and‐k distributions, a toggle switch model from systems biology, a queuing model and a Lévy‐driven stochastic volatility model.

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Section: Toggle Switch Modelmentioning

confidence: 99%

“…5 in Bonassi and West (2015). We compare our method using p = 1 with a summary-based approach using the 11-dimensional tailor-made summary statistic from Bonassi et al (2011) and Bonassi and West (2015). Since the data are one dimensional, the Wasserstein distance between data sets can be computed quickly via sorting.…”

Section: Toggle Switch Modelmentioning

confidence: 99%

Approximate Bayesian Computation with the Wasserstein Distance

Bernton

Jacob

Gerber

et al. 2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

113

145

View full text Add to dashboard Cite

show abstract

“…1 fit our model's parameters, but suffered low acceptance rates (frequent rejection at 2aiii), and was slow to deliver the full particle sample. We therefore used a modified ABC‐SMC with adaptive weighting, ABC‐SMC‐AW (Bonassi and West ). ABC‐SMC‐AW alters the weighting ω j of each particle p j according to the value of the metric

, drawing particles with new weights v j at step 2ai in Eq.…”

Section: Methodsmentioning

confidence: 99%

“…The first and second processes relate to recruitment: we chose to determine the probability of juvenile occurrence by climate, and the annual recruitment rate using conspecific density and competitive factors. Fitting these two separately (following Zhu et al ) avoided overfitting and allowed us to make best use of the data available by incorporating all inventory information on stems < 7.5 cm DBH. The probability of juvenile occurrence was estimated using an MCMC approach on inventory presence/absence data, and recruitment, growth and mortality rates were estimated using the ABC approach with a forest simulator (the PPA) and inventory juvenile count data.…”

Section: Methodsmentioning

confidence: 99%

Capturing juvenile tree dynamics from count data using Approximate Bayesian Computation

et al. 2019

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The juvenile life stage is a crucial determinant of forest dynamics and a first indicator of changes to species' ranges under climate change. However, paucity of detailed re‐measurement data of seedlings, saplings and small trees means that their demography is not well understood at large scales, and rarely represented in forest models in detail. In this study we quantify the effects of climate and density dependence on recruitment and juvenile growth and mortality rates of thirteen species measured in the Spanish Forest Inventory. Single‐census sapling count data is used to constrain demographic parameters of a simple forest juvenile dynamics model based on the perfect plasticity approximation model (PPA) within a likelihood‐free parameterisation method, Approximate Bayesian Computation. Our results highlight marked differences between species, and the important role of climate and stand structure, in controlling juvenile dynamics. Recruitment had a hump‐shaped relationship with conspecific density, and for most species conspecific competition had a stronger negative effect than heterospecific competition. Mediterranean species showed on average higher mortality and lower growth rates than temperate species, and in low density stands recruitment and mortality rates were positively correlated. Under climate change our model predicted declines in recruitment rates for almost all species. Reliable predictive models of forest dynamics should include realistic representation of critical early life‐stage processes and our approach demonstrates that existing coarse count data can be used to parameterise such models. Approximate Bayesian Computation may have wide application in many fields of ecology to unlock information about past processes from single survey observations.

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“…ABC methods have been applied in several fields of science and engineering for Bayesian inference. They have been employed for statistical inference in systems biology [12], ecological models [13] and were also applied by [14] in problems of parameter inference and model selection for dynamical models.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Probabilistic Power Flow Analysis Using Jacobian Approximate Bayesian Computation

Zuluaga

Álvarez

2018

IEEE Trans. Power Syst.

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Abstract-A probabilistic power flow (PPF) study is an essential tool for the analysis and planning of a power system when specific variables are considered as random variables with particular probability distributions. The most widely used method for solving the PPF problem is Monte Carlo simulation (MCS). Although MCS is accurate for obtaining the uncertainty of the state variables, it is also computationally expensive, since it relies on repetitive deterministic power flow solutions. In this paper, we introduce a different perspective for the PPF problem. We frame the PPF as a probabilistic inference problem, and instead of repetitively solving optimization problems, we use Bayesian inference for computing posterior distributions over state variables. Additionally, we provide a likelihood-free method based on the Approximate Bayesian Computation philosophy, that incorporates the Jacobian computed from the power flow equations. Results in three different test systems show that the proposed methodologies are competitive alternatives for solving the PPF problem, and in some cases, they allow for reduction in computation time when compared to MCS.

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Sequential Monte Carlo with Adaptive Weights for Approximate Bayesian Computation

Cited by 51 publications

References 33 publications

Approximate Bayesian Computation with the Wasserstein Distance

Approximate Bayesian Computation with the Wasserstein Distance

Capturing juvenile tree dynamics from count data using Approximate Bayesian Computation

Bayesian Probabilistic Power Flow Analysis Using Jacobian Approximate Bayesian Computation

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