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Friel, Nial
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Friel, Nial
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Friel, Nial
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Now showing 1 - 4 of 4
- PublicationInformed sub-sampling MCMC: approximate Bayesian inference for large datasetsThis paper introduces a framework for speeding up Bayesian inference conducted in presence of large datasets. We design a Markov chain whose transition kernel uses an unknown fraction of fixed size of the available data that is randomly refreshed throughout the algorithm. Inspired by the Approximate Bayesian Computation literature, the subsampling process is guided by the fidelity to the observed data, as measured by summary statistics. The resulting algorithm, Informed Sub-Sampling MCMC, is a generic and flexible approach which, contrary to existing scalable methodologies, preserves the simplicity of the Metropolis–Hastings algorithm. Even though exactness is lost, i.e the chain distribution approximates the posterior, we study and quantify theoretically this bias and show on a diverse set of examples that it yields excellent performances when the computational budget is limited. If available and cheap to compute, we show that setting the summary statistics as the maximum likelihood estimator is supported by theoretical arguments.
282Scopus© Citations 5 - PublicationBayesian Model Selection for Exponential Random Graph Models via Adjusted PseudolikelihoodsModels with intractable likelihood functions arise in areas including network analysisand spatial statistics, especially those involving Gibbs random fields. Posterior parameter estimationin these settings is termed a doubly-intractable problem because both the likelihoodfunction and the posterior distribution are intractable. The comparison of Bayesian models isoften based on the statistical evidence, the integral of the un-normalised posterior distributionover the model parameters which is rarely available in closed form. For doubly-intractablemodels, estimating the evidence adds another layer of difficulty. Consequently, the selectionof the model that best describes an observed network among a collection of exponentialrandom graph models for network analysis is a daunting task. Pseudolikelihoods offer atractable approximation to the likelihood but should be treated with caution because they canlead to an unreasonable inference. This paper specifies a method to adjust pseudolikelihoodsin order to obtain a reasonable, yet tractable, approximation to the likelihood. This allowsimplementation of widely used computational methods for evidence estimation and pursuitof Bayesian model selection of exponential random graph models for the analysis of socialnetworks. Empirical comparisons to existing methods show that our procedure yields similarevidence estimates, but at a lower computational cost.
379Scopus© Citations 14 - PublicationEfficient Bayesian inference for exponential random graph models by correcting the pseudo-posterior distributionExponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves the calculation of an intractable normalizing constant. This barrier motivates the consideration of tractable approximations to the likelihood function, such as the pseudolikelihood function, which offers an approach to constructing such an approximation. Naive implementation of what we term a pseudo-posterior resulting from replacing the likelihood function in the posterior distribution by the pseudolikelihood is likely to give misleading inferences. We provide practical guidelines to correct a sample from such a pseudo-posterior distribution so that it is approximately distributed from the target posterior distribution and discuss the computational and statistical efficiency that result from this approach. We illustrate our methodology through the analysis of real-world graphs. Comparisons against the approximate exchange algorithm of Caimo and Friel (2011) are provided, followed by concluding remarks.
212Scopus© Citations 18 - PublicationModel comparison for Gibbs random fields using noisy reversible jump Markov chain Monte CarloThe reversible jump Markov chain Monte Carlo (RJMCMC) method offers an across-model simulation approach for Bayesian estimation and model comparison, by exploring the sampling space that consists of several models of possibly varying dimensions. A naive implementation of RJMCMC to models like Gibbs random fields suffers from computational difficulties: the posterior distribution for each model is termed doubly-intractable since computation of the likelihood function is rarely available. Consequently, it is simply impossible to simulate a transition of the Markov chain in the presence of likelihood intractability. A variant of RJMCMC is presented, called noisy RJMCMC, where the underlying transition kernel is replaced with an approximation based on unbiased estimators. Based on previous theoretical developments, convergence guarantees for the noisy RJMCMC algorithm are provided. The experiments show that the noisy RJMCMC algorithm can be much more efficient than other exact methods, provided that an estimator with controlled Monte Carlo variance is used, a fact which is in agreement with the theoretical analysis.
348Scopus© Citations 2