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In the following article we consider approximate Bayesian parameter inference for observation driven time series models. Such statistical models appear in a wide variety of applications, including econometrics and applied mathematics. This…

Computation · Statistics 2013-04-01 Ajay Jasra , Nikolas Kantas , Elena Ehrlich

Bayesian inference with stochastic models is often difficult because their likelihood functions involve high-dimensional integrals. Approximate Bayesian Computation (ABC) avoids evaluating the likelihood function and instead infers model…

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) have become a essential tool for the analysis of complex stochastic models. Earlier, Grelaud et al. (2009) advocated the use of ABC for Bayesian model choice in the specific case of Gibbs random…

Methodology · Statistics 2015-03-19 Christian P. Robert , Jean-Marie Cornuet , Jean-Michel Marin , Natesh Pillai

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

Approximate Bayesian computation (ABC) methods, which are applicable when the likelihood is difficult or impossible to calculate, are an active topic of current research. Most current ABC algorithms directly approximate the posterior…

Computation · Statistics 2012-12-10 Y. Fan , D. J. Nott , S. A. Sisson

Approximate Bayesian computation (ABC) is a popular technique for approximating likelihoods and is often used in parameter estimation when the likelihood functions are analytically intractable. Although the use of ABC is widespread in many…

Statistics Theory · Mathematics 2011-03-29 Thomas A. Dean , Sumeetpal S. Singh , Ajay Jasra , Gareth W. Peters

Approximate Bayesian computation (ABC), also known as likelihood-free methods, have become a favourite tool for the analysis of complex stochastic models, primarily in population genetics but also in financial analyses. We advocated in…

Computation · Statistics 2015-03-18 Christian Robert , Jean-Michel Marin , Natesh S. Pillai

Composite likelihood provides approximate inference when the full likelihood is intractable and sub-likelihood functions of marginal events can be evaluated relatively easily. It has been successfully applied for many complex models.…

Methodology · Statistics 2024-09-05 Wentao Li , Rosabeth White , Dennis Prangle

Stochastic systems in biology often exhibit substantial variability within and between cells. This variability, as well as having dramatic functional consequences, provides information about the underlying details of the system's behaviour.…

Quantitative Methods · Quantitative Biology 2015-11-09 Iain G. Johnston

pocoMC is a Python package for accelerated Bayesian inference in astronomy and cosmology. The code is designed to sample efficiently from posterior distributions with non-trivial geometry, including strong multimodality and non-linearity.…

Instrumentation and Methods for Astrophysics · Physics 2022-07-13 Minas Karamanis , David Nabergoj , Florian Beutler , John A. Peacock , Uros Seljak

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

This Chapter, "A Guide to General-Purpose ABC Software", is to appear in the forthcoming Handbook of Approximate Bayesian Computation (2018). We present general-purpose software to perform Approximate Bayesian Computation (ABC) as…

Computation · Statistics 2018-06-22 Athanasios Kousathanas , Pablo Duchen , Daniel Wegmann

Approximate Bayesian Computation (ABC) methods are applicable to statistical models specified by generative processes with analytically intractable likelihoods. These methods try to approximate the posterior density of a model parameter by…

Methodology · Statistics 2024-03-11 Sanjay Chaudhuri , Subhroshekhar Ghosh , Kim Cuc Pham

Controlled branching processes are stochastic growth population models in which the number of individuals with reproductive capacity in each generation is controlled by a random control function. The purpose of this work is to examine the…

Methodology · Statistics 2019-07-03 M. González , R. Martínez , C. Minuesa , I. del Puerto

Approximate Bayesian computation (ABC) has become an essential part of the Bayesian toolbox for addressing problems in which the likelihood is prohibitively expensive or entirely unknown, making it intractable. ABC defines a…

Methodology · Statistics 2020-07-14 Hien D. Nguyen , Julyan Arbel , Hongliang Lü , Florence Forbes

A growing number of generative statistical models do not permit the numerical evaluation of their likelihood functions. Approximate Bayesian computation (ABC) has become a popular approach to overcome this issue, in which one simulates…

Methodology · Statistics 2019-05-10 Espen Bernton , Pierre E. Jacob , Mathieu Gerber , Christian P. Robert

Approximate Bayesian Computation (ABC) provides methods for Bayesian inference in simulation-based stochastic models which do not permit tractable likelihoods. We present a new ABC method which uses probabilistic neural emulator networks to…

Machine Learning · Statistics 2019-05-21 Jan-Matthis Lueckmann , Giacomo Bassetto , Theofanis Karaletsos , Jakob H. Macke

The goal of this paper is to explore the basic Approximate Bayesian Computation (ABC) algorithm via the lens of information theory. ABC is a widely used algorithm in cases where the likelihood of the data is hard to work with or…

Methodology · Statistics 2019-08-14 Konstantinos Spiliopoulos

The popularity of Bayesian statistical methods has increased dramatically in recent years across many research areas and industrial applications. This is the result of a variety of methodological advances with faster and cheaper hardware as…

Computation · Statistics 2022-01-12 Tomás Capretto , Camen Piho , Ravin Kumar , Jacob Westfall , Tal Yarkoni , Osvaldo A. Martin
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