Adaptive approximate Bayesian computation

Beaumont, Mark A.; Cornuet, Jean‐Marie; Marin, Jean‐Michel; Robert, Christian P.

doi:10.1093/biomet/asp052

Cited by 472 publications

(596 citation statements)

References 11 publications

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“…Recall that the simulated version of BIL takes the form given in eq. (10). For the computation of the ABC estimator, this requires computation of Z s n = Z n (θ s ) for each draw θ s from the posterior, where…”

Section: Model-based Statisticsmentioning

confidence: 99%

ABC of SV: Limited information likelihood inference in stochastic volatility jump-diffusion models

Creel

Kristensen

2015

Journal of Empirical Finance

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We develop novel methods for estimation and filtering of continuous-time models with stochastic volatility and jumps using so-called Approximate Bayesian Computation which build likelihoods based on limited information. The proposed estimators and filters are computationally attractive relative to standard likelihood-based versions since they rely on low-dimensional auxiliary statistics and so avoid computation of high-dimensional integrals. Despite their computational simplicity, we find that estimators and filters perform well in practice and lead to precise estimates of model parameters and latent variables. We show how the methods can incorporate intra-daily information to improve on the estimation and filtering. In particular, the availability of realized volatility measures help us in learning about parameters and latent states. The method is employed in the estimation of a flexible stochastic volatility model for the dynamics of the S&P 500 equity index. We find evidence of the presence of a dynamic jump rate and in favor of a structural break in parameters at the time of the recent financial crisis. We find evidence that possible measurement error in log price is small and has little effect on parameter estimates. Smoothing shows that, recently, volatility and the jump rate have returned to the low levels of 2004-2006.

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Section: Model-based Statisticsmentioning

confidence: 99%

ABC of SV: Limited information likelihood inference in stochastic volatility jump-diffusion models

Creel

Kristensen

2015

Journal of Empirical Finance

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“…This technique can be improved by combining ABC with population Monte Carlo (PMC 7 , Beaumont et al 2009;Cameron & Pettitt 2012;Weyant et al 2013). Until now, ABC seems to already have various applications in biology-related domains (e.g., Beaumont et al 2009;Berger et al 2010;Csilléry et al 2010;Drovandi & Pettitt 2011), while applications for astronomical purposes are few: morphological transformation of galaxies (Cameron & Pettitt 2012), cosmological parameter inference using type Ia supernovae (Weyant et al 2013), constraints of the disk formation of the Milky Way (Robin et al 2014), and strong lensing properties of galaxy clusters (Killedar et al 2015). Very recently, two papers (Ishida et al 2015;Akeret et al 2015) dedicated to ABC in a general cosmological context have been submitted.…”

Section: Introductionmentioning

confidence: 99%

A new model to predict weak-lensing peak counts

Lin

Kilbinger

2015

A&A

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Context. Peak counts have been shown to be an excellent tool for extracting the non-Gaussian part of the weak lensing signal. Recently, we developed a fast stochastic forward model to predict weak-lensing peak counts. Our model is able to reconstruct the underlying distribution of observables for analysis. Aims. In this work, we explore and compare various strategies for constraining a parameter using our model, focusing on the matter density Ω m and the density fluctuation amplitude σ 8 . Methods. First, we examine the impact from the cosmological dependency of covariances (CDC). Second, we perform the analysis with the copula likelihood, a technique that makes a weaker assumption than does the Gaussian likelihood. Third, direct, non-analytic parameter estimations are applied using the full information of the distribution. Fourth, we obtain constraints with approximate Bayesian computation (ABC), an efficient, robust, and likelihood-free algorithm based on accept-reject sampling. Results. We find that neglecting the CDC effect enlarges parameter contours by 22% and that the covariance-varying copula likelihood is a very good approximation to the true likelihood. The direct techniques work well in spite of noisier contours. Concerning ABC, the iterative process converges quickly to a posterior distribution that is in excellent agreement with results from our other analyses. The time cost for ABC is reduced by two orders of magnitude. Conclusions. The stochastic nature of our weak-lensing peak count model allows us to use various techniques that approach the true underlying probability distribution of observables, without making simplifying assumptions. Our work can be generalized to other observables where forward simulations provide samples of the underlying distribution.

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“…We focus on approximate Bayesian computation (ABC), a particular likelihood-free inference method, introduced by Pritchard et al (1999) in the biology literature. For full details, as well as generalizations and improvements, we refer to that paper as well as Blum et al (2012) and Beaumont et al (2009). Thus far, ABC has found limited use in astronomy settings, as in Cameron and Pettitt (2012) and Weyant et al (2013).…”

Section: Methodsologymentioning

confidence: 99%

The potential of likelihood-free inference of cosmological parameters with weak lensing data

Vespe

2014

Proc. IAU

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Abstract. In the statistical framework of likelihood-free inference, the posterior distribution of model parameters is explored via simulation rather than direct evaluation of the likelihood function, permitting inference in situations where this function is analytically intractable. We consider the problem of estimating cosmological parameters using measurements of the weak gravitational lensing of galaxies; specifically, we propose the use a likelihood-free approach to investigate the posterior distribution of some parameters in the ΛCDM model upon observing a large number of sheared galaxies. The choice of summary statistic used when comparing observed data and simulated data in the likelihood-free inference framework is critical, so we work toward a principled method of choosing the summary statistic, aiming for dimension reduction while seeking a statistic that is as close as possible to being sufficient for the parameters of interest.

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Adaptive approximate Bayesian computation

Cited by 472 publications

References 11 publications

ABC of SV: Limited information likelihood inference in stochastic volatility jump-diffusion models

ABC of SV: Limited information likelihood inference in stochastic volatility jump-diffusion models

A new model to predict weak-lensing peak counts

The potential of likelihood-free inference of cosmological parameters with weak lensing data

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