Approximate Bayesian Computation by Subset Simulation using hierarchical state-space models

2017 ◽  
Vol 84 ◽  
pp. 2-20 ◽  
Author(s):  
Majid K. Vakilzadeh ◽  
Yong Huang ◽  
James L. Beck ◽  
Thomas Abrahamsson
Keyword(s):  
State Space ◽  
Approximate Bayesian Computation ◽  
State Space Models ◽  
Bayesian Computation ◽  
Subset Simulation ◽  
Approximate Bayesian

scholarly journals Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models

2019 ◽  
Vol 28 (3) ◽  
pp. 508-522 ◽  
Author(s):  
Gael M. Martin ◽  
Brendan P. M. McCabe ◽  
David T. Frazier ◽  
Worapree Maneesoonthorn ◽  
Christian P. Robert
Keyword(s):  
State Space ◽  
Approximate Bayesian Computation ◽  
State Space Models ◽  
Bayesian Computation ◽  
Approximate Bayesian

scholarly journals Probabilistic Updating of Structural Models for Damage Assessment Using Approximate Bayesian Computation

Sensors ◽  
2020 ◽  
Vol 20 (11) ◽  
pp. 3197 ◽  
Author(s):  
Zhouquan Feng ◽  
Yang Lin ◽  
Wenzan Wang ◽  
Xugang Hua ◽  
Zhengqing Chen
Keyword(s):  
Damage Assessment ◽  
Approximate Bayesian Computation ◽  
Model Updating ◽  
Likelihood Function ◽  
Probabilistic Approach ◽  
Model Parameters ◽  
Bayesian Computation ◽  
The Novel ◽  
Subset Simulation ◽  
Approximate Bayesian

A novel probabilistic approach for model updating based on approximate Bayesian computation with subset simulation (ABC-SubSim) is proposed for damage assessment of structures using modal data. The ABC-SubSim is a likelihood-free Bayesian approach in which the explicit expression of likelihood function is avoided and the posterior samples of model parameters are obtained using the technique of subset simulation. The novel contributions of this paper are on three fronts: one is the introduction of some new stopping criteria to find an appropriate tolerance level for the metric used in the ABC-SubSim; the second one is the employment of a hybrid optimization scheme to find finer optimal values for the model parameters; and the last one is the adoption of an iterative approach to determine the optimal weighting factors related to the residuals of modal frequency and mode shape in the metric. The effectiveness of this approach is demonstrated using three illustrative examples.

scholarly journals Approximate Bayesian Computation by Subset Simulation

2014 ◽  
Vol 36 (3) ◽  
pp. A1339-A1358 ◽  
Author(s):  
Manuel Chiachio ◽  
James L. Beck ◽  
Juan Chiachio ◽  
Guillermo Rus
Keyword(s):  
Approximate Bayesian Computation ◽  
Bayesian Computation ◽  
Subset Simulation ◽  
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.

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