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This preprint has been reviewed and recommended by Peer Community In Evolutionary Biology (http://dx.doi.org/10.24072/pci.evolbiol.100036). Approximate Bayesian computation (ABC) has grown into a standard methodology that manages Bayesian…

In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The algorithm, which we termed the "Bayesian Inverse Monte Carlo…

Computation · Statistics 2019-11-06 Siddhant Wahal , George Biros

Approximate Bayesian Computation (ABC) are likelihood-free Monte Carlo methods. ABC methods use a comparison between simulated data, using different parameters drew from a prior distribution, and observed data. This comparison process is…

Machine Learning · Statistics 2015-03-31 Carlos D. Zuluaga , Edgar A. Valencia , Mauricio A. Álvarez

The frequentist method of simulated minimum distance (SMD) is widely used in economics to estimate complex models with an intractable likelihood. In other disciplines, a Bayesian approach known as Approximate Bayesian Computation (ABC) is…

Methodology · Statistics 2017-11-16 Jean-Jacques Forneron , Serena Ng

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC…

Methodology · Statistics 2013-06-12 M. G. B. Blum , M. A. Nunes , D. Prangle , S. A. Sisson

For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations…

Computation · Statistics 2011-07-04 Chris Barnes , Sarah Filippi , Michael P. H. Stumpf , Thomas Thorne

Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard…

Methodology · Statistics 2014-08-06 Umberto Picchini

Background: When conducting a meta-analysis of a continuous outcome, estimated means and standard deviations from the selected studies are required in order to obtain an overall estimate of the mean effect and its confidence interval. If…

Methodology · Statistics 2020-04-07 Deukwoo Kwon , Isildinha M. Reis

ABC algorithms are notoriously expensive in computing time, as they require simulating many complete artificial datasets from the model. We advocate in this paper a "divide and conquer" approach to ABC, where we split the likelihood into n…

Computation · Statistics 2015-12-02 Simon Barthelmé , Nicolas Chopin , Vincent Cottet

By the nature of their construction, many statistical models for extremes result in likelihood functions that are computationally prohibitive to evaluate. This is consequently problematic for the purposes of likelihood-based inference. With…

Methodology · Statistics 2014-11-07 Robert Erhardt , Scott A. Sisson

This paper introduces a simple, general framework for likelihood-free Bayesian reinforcement learning, through Approximate Bayesian Computation (ABC). The main advantage is that we only require a prior distribution on a class of simulators…

Machine Learning · Statistics 2013-07-01 Christos Dimitrakakis , Nikolaos Tziortziotis

In this paper we propose and study local linear and polynomial based estimators for implementing Approximate Bayesian Computation (ABC) style indirect inference and GMM estimators. This method makes use of nonparametric regression in the…

Statistics Theory · Mathematics 2020-03-13 Michael Creel , Jiti Gao , Han Hong , Dennis Kristensen

Approximate Bayesian Computation (ABC) methods are used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Both the accuracy and computational efficiency of ABC depend on the choice of…

Methodology · Statistics 2017-03-17 Bai Jiang , Tung-yu Wu , Charles Zheng , Wing H. Wong

Simulation-Based Inference (SBI) is a common name for an emerging family of approaches that infer the model parameters when the likelihood is intractable. Existing SBI methods either approximate the likelihood, such as Approximate Bayesian…

Machine Learning · Computer Science 2023-11-29 Theo Gruner , Boris Belousov , Fabio Muratore , Daniel Palenicek , Jan Peters

Approximate Bayesian computation (ABC) is a likelihood-free inference method that has been employed in various applications. However, ABC can be sensitive to outliers if a data discrepancy measure is chosen inappropriately. In this paper,…

Machine Learning · Statistics 2021-03-08 Masahiro Fujisawa , Takeshi Teshima , Issei Sato , Masashi Sugiyama

Approximate Bayesian computation (ABC) is a class of algorithmic methods in Bayesian inference using statistical summaries and computer simulations. ABC has become popular in evolutionary genetics and in other branches of biology. However…

Computation · Statistics 2011-05-03 Olivier Francois , Guillaume Laval

Approximate Bayesian Computation (ABC) enables parameter inference for complex physical systems in cases where the true likelihood function is unknown, unavailable, or computationally too expensive. It relies on the forward simulation of…

Cosmology and Nongalactic Astrophysics · Physics 2019-08-13 E. E. O. Ishida , S. D. P. Vitenti , M. Penna-Lima , J. Cisewski , R. S. de Souza , A. M. M. Trindade , E. Cameron , V. C. Busti

Approximate Bayesian computation (ABC) methods are used to approximate posterior distributions using simulation rather than likelihood calculations. We introduce Gaussian process (GP) accelerated ABC, which we show can significantly reduce…

Computation · Statistics 2014-02-25 Richard D Wilkinson

Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic…

Methodology · Statistics 2025-01-27 Henri Pesonen , Jukka Corander

The Ensemble Kalman inversion (EKI) method is a method for the estimation of unknown parameters in the context of (Bayesian) inverse problems. The method approximates the underlying measure by an ensemble of particles and iteratively…

Numerical Analysis · Mathematics 2021-08-02 Dirk Blömker , Claudia Schillings , Philipp Wacker , Simon Weissmann
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