96,057 research outputs found
Asymptotic Properties of Approximate Bayesian Computation
Approximate Bayesian computation allows for statistical analysis in models
with intractable likelihoods. In this paper we consider the asymptotic
behaviour of the posterior distribution obtained by this method. We give
general results on the rate at which the posterior distribution concentrates on
sets containing the true parameter, its limiting shape, and the asymptotic
distribution of the posterior mean. These results hold under given rates for
the tolerance used within the method, mild regularity conditions on the summary
statistics, and a condition linked to identification of the true parameters.
Implications for practitioners are discussed.Comment: This 31 pages paper is a revised version of the paper, including
supplementary materia
Efficient learning in Approximate Bayesian Computation
Efficient learning in Approximate Bayesian Computatio
Regression approaches for Approximate Bayesian Computation
This book chapter introduces regression approaches and regression adjustment
for Approximate Bayesian Computation (ABC). Regression adjustment adjusts
parameter values after rejection sampling in order to account for the imperfect
match between simulations and observations. Imperfect match between simulations
and observations can be more pronounced when there are many summary statistics,
a phenomenon coined as the curse of dimensionality. Because of this imperfect
match, credibility intervals obtained with regression approaches can be
inflated compared to true credibility intervals. The chapter presents the main
concepts underlying regression adjustment. A theorem that compares theoretical
properties of posterior distributions obtained with and without regression
adjustment is presented. Last, a practical application of regression adjustment
in population genetics shows that regression adjustment shrinks posterior
distributions compared to rejection approaches, which is a solution to avoid
inflated credibility intervals.Comment: Book chapter, published in Handbook of Approximate Bayesian
Computation 201
Approximate Bayesian Computation by Subset Simulation
A new Approximate Bayesian Computation (ABC) algorithm for Bayesian updating
of model parameters is proposed in this paper, which combines the ABC
principles with the technique of Subset Simulation for efficient rare-event
simulation, first developed in S.K. Au and J.L. Beck [1]. It has been named
ABC- SubSim. The idea is to choose the nested decreasing sequence of regions in
Subset Simulation as the regions that correspond to increasingly closer
approximations of the actual data vector in observation space. The efficiency
of the algorithm is demonstrated in two examples that illustrate some of the
challenges faced in real-world applications of ABC. We show that the proposed
algorithm outperforms other recent sequential ABC algorithms in terms of
computational efficiency while achieving the same, or better, measure of ac-
curacy in the posterior distribution. We also show that ABC-SubSim readily
provides an estimate of the evidence (marginal likelihood) for posterior model
class assessment, as a by-product
Scalable Inference for Markov Processes with Intractable Likelihoods
Bayesian inference for Markov processes has become increasingly relevant in
recent years. Problems of this type often have intractable likelihoods and
prior knowledge about model rate parameters is often poor. Markov Chain Monte
Carlo (MCMC) techniques can lead to exact inference in such models but in
practice can suffer performance issues including long burn-in periods and poor
mixing. On the other hand approximate Bayesian computation techniques can allow
rapid exploration of a large parameter space but yield only approximate
posterior distributions. Here we consider the combined use of approximate
Bayesian computation (ABC) and MCMC techniques for improved computational
efficiency while retaining exact inference on parallel hardware
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