Bayesian Inference from Composite Likelihoods, with an Application to Spatial Extremes

By Mathieu Ribatet, Daniel Cooley, A. C. Davison. 2009

198 citations recorded by the source corpus.

Composite likelihoods are increasingly used in applications where the full likelihood is analytically unknown or computationally prohibitive. Although the maximum composite likelihood estimator has frequentist properties akin to those of the usual maximum likelihood estimator, Bayesian inference based on composite likelihoods has yet to be explored. In this paper we investigate the use of the Metropolis--Hastings algorithm to compute a pseudo-posterior distribution based on the composite likelihood. Two methodologies for adjusting the algorithm are presented and their performance on approximating the true posterior distribution is investigated using simulated data sets and real data on spatial extremes of rainfall.

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Citations in the corpus

Bayesian estimation of rainfall intensity-duration-frequency relationships (2015, methodology): “Curvature adjustment (Ribatet et al., 2012) Determine C 2 Rp p in lcurvc ðx;wÞ ¼ lcðx; ŵÞ; ŵ ¼ ŵc þ C ðw ŵcÞ; ðA:6Þ such that the usual property Eq.”
Composite Likelihood Methods (2012, background): “In the discussion on the Friday morning of the workshop, it was mentioned that for pairwise likelihood, J(θ) − H(θ) tends to be positive definite when the parameter θ represents positive dependence; see the Appendix of Ribatet et al (2012) for the context of a Markov process.”
Bayesian hierarchical modeling of extreme hourly precipitation in Norway (2013, methodology): “We note that more involved methodologies (see e.g. Sang & Gelfand, 2009; Ribatet et al., 2012; Ghosh & Mallick, 2011, among others) would be capable of incorporating such residual dependence.”
Spatial Bayesian hierarchical modeling of precipitation extremes over a large domain (2015, background): “Max-stable processes [Schlather, 2002; Cooley et al., 2006; Shang et al., 2011; Ribatet et al., 2012; Padoan et al., 2010; Sang, 2015] refer to the specification of a joint distribution that is specifically formulated for spatial extreme data.”
Calibrating general posterior credible regions (2015, methodology): “ted version of the latter, where the scaling parameter return by our posterior calibration algorithm is != 0:015. The two marginal posterior density plots in Panels (a) and (b) match what is shown in Ribatet et al. (2012). Our calibrated posterior exactly matches the full posterior for , but is a bi”
An M‐estimator of spatial tail dependence (2014, methodology): “wise monthly or annual maxima using composite likelihood methods. This is done either in a frequentist setting (Padoan et al., 2010; Davison et al., 2012) or in a Bayesian one (Reich and Shaby, 2012; Cooley et al., 2012). Alternatively, Yuen and Stoev (2014) propose an M-estimator based on nite-dime”
Bayesian Few-Shot Classification with One-vs-Each Pólya-Gamma Augmented Gaussian Processes (2020, background): “Prior work on Bayesian inference with composite likelihoods has shown that the composite posterior is consistent under fairly general conditions for correctly specified models (Miller, 2019) but can produce overly concentrated posteriors (Pauli et al., 2011; Ribatet et al., 2012) since each componen”
Statistical Modelling of Spatial Extremes (2012, methodology): “See also Smith and Stephenson (2009) and Ribatet et al. (2012), who use Bayes’ theorem and pairwise likelihood to fit extremal models to rainfall data.”
Spatial extremes: Max-stable processes at work (2013, methodology): “Likelihood based inferences are widely used either in a frequentist context Genton et al. (2011); Davison et al. (2012); Padoan et al. (2010) or in a Bayesian framework Ribatet et al. (2012); Erhardt and Smith (2012).”
Geostatistics of Dependent and Asymptotically Independent Extremes (2013, methodology): “From the Bayesian perspective, Ribatet et al. (2012) have developed a Monte Carlo Markov chain algorithm for fitting such models by sampling the composite posterior distribution using a modified acceptance rate.”