Approximate Bayesian Computation and MCMC

2004 ◽  
pp. 99-113 ◽  
Author(s):  
Vincent Plagnol ◽  
Simon Tavaré
Keyword(s):  
Approximate Bayesian Computation ◽  
Bayesian Computation ◽  
Approximate Bayesian

scholarly journals Weighted approximate Bayesian computation via Sanov’s theorem

2021 ◽  
Author(s):  
Cecilia Viscardi ◽  
Michele Boreale ◽  
Fabio Corradi
Keyword(s):  
Large Deviations ◽  
Posterior Distribution ◽  
Approximate Bayesian Computation ◽  
Bayesian Computation ◽  
Information Theoretic ◽  
Discrete Random Variables ◽  
Positive Weights ◽  
Approximate Bayesian ◽  
Information Theoretic Method ◽  
Computational Resources

AbstractWe consider the problem of sample degeneracy in Approximate Bayesian Computation. It arises when proposed values of the parameters, once given as input to the generative model, rarely lead to simulations resembling the observed data and are hence discarded. Such “poor” parameter proposals do not contribute at all to the representation of the parameter’s posterior distribution. This leads to a very large number of required simulations and/or a waste of computational resources, as well as to distortions in the computed posterior distribution. To mitigate this problem, we propose an algorithm, referred to as the Large Deviations Weighted Approximate Bayesian Computation algorithm, where, via Sanov’s Theorem, strictly positive weights are computed for all proposed parameters, thus avoiding the rejection step altogether. In order to derive a computable asymptotic approximation from Sanov’s result, we adopt the information theoretic “method of types” formulation of the method of Large Deviations, thus restricting our attention to models for i.i.d. discrete random variables. Finally, we experimentally evaluate our method through a proof-of-concept implementation.

Flow parameter estimation using laser absorption spectroscopy and approximate Bayesian computation

2021 ◽  
Vol 62 (2) ◽  
Author(s):  
Jason D. Christopher ◽  
Olga A. Doronina ◽  
Dan Petrykowski ◽  
Torrey R. S. Hayden ◽  
Caelan Lapointe ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Absorption Spectroscopy ◽  
Approximate Bayesian Computation ◽  
Flow Parameter ◽  
Bayesian Computation ◽  
Laser Absorption Spectroscopy ◽  
Laser Absorption ◽  
Approximate Bayesian

scholarly journals Approximate Bayesian Computation for Discrete Spaces

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 312
Author(s):  
Ilze A. Auzina ◽  
Jakub M. Tomczak
Keyword(s):  
Approximate Bayesian Computation ◽  
Likelihood Function ◽  
Real Life ◽  
Random Variables ◽  
Bayesian Computation ◽  
Inference Problem ◽  
Markov Kernel ◽  
Inference Problems ◽  
Binary Neural Network ◽  
Approximate Bayesian

Many real-life processes are black-box problems, i.e., the internal workings are inaccessible or a closed-form mathematical expression of the likelihood function cannot be defined. For continuous random variables, likelihood-free inference problems can be solved via Approximate Bayesian Computation (ABC). However, an optimal alternative for discrete random variables is yet to be formulated. Here, we aim to fill this research gap. We propose an adjusted population-based MCMC ABC method by re-defining the standard ABC parameters to discrete ones and by introducing a novel Markov kernel that is inspired by differential evolution. We first assess the proposed Markov kernel on a likelihood-based inference problem, namely discovering the underlying diseases based on a QMR-DTnetwork and, subsequently, the entire method on three likelihood-free inference problems: (i) the QMR-DT network with the unknown likelihood function, (ii) the learning binary neural network, and (iii) neural architecture search. The obtained results indicate the high potential of the proposed framework and the superiority of the new Markov kernel.

scholarly journals Complex genetic admixture histories reconstructed with Approximate Bayesian Computation

2021 ◽  
Author(s):  
Cesar A. Fortes‐Lima ◽  
Romain Laurent ◽  
Valentin Thouzeau ◽  
Bruno Toupance ◽  
Paul Verdu
Keyword(s):  
Approximate Bayesian Computation ◽  
Genetic Admixture ◽  
Bayesian Computation ◽  
Approximate Bayesian

scholarly journals Cophylogeny Reconstruction via an Approximate Bayesian Computation

2014 ◽  
Vol 64 (3) ◽  
pp. 416-431 ◽  
Author(s):  
C. Baudet ◽  
B. Donati ◽  
B. Sinaimeri ◽  
P. Crescenzi ◽  
C. Gautier ◽  
...  
Keyword(s):  
Approximate Bayesian Computation ◽  
Bayesian Computation ◽  
Approximate Bayesian

scholarly journals Hierarchical Approximate Bayesian Computation

Psychometrika ◽  
2013 ◽  
Vol 79 (2) ◽  
pp. 185-209 ◽  
Author(s):  
Brandon M. Turner ◽  
Trisha Van Zandt
Keyword(s):  
Approximate Bayesian Computation ◽  
Bayesian Computation ◽  
Approximate Bayesian
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