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

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

Approximate Bayesian Computation with composite score functions

Both Approximate Bayesian Computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score functions as summary statistics in ABC in order to obtain accurate approximations to the posterior distribution. This is motivated by the use of the score function of the full likelihood, and extended to general unbiased estimating functions in complex models. Moreover, we show that if the composite score is suitably standardised, the resulting ABC procedure is invariant to reparameterisations and automatically adjusts the curvature of the composite likelihood, and of the corresponding posterior distribution. The method is illustrated through examples with simulated data, and an application to modelling of spatial extreme rainfall data is discussed.Comment: Statistics and Computing (final version

Calibration of conditional composite likelihood for Bayesian inference on Gibbs random fields

Gibbs random fields play an important role in statistics, however, the resulting likelihood is typically unavailable due to an intractable normalizing constant. Composite likelihoods offer a principled means to construct useful approximations. This paper provides a mean to calibrate the posterior distribution resulting from using a composite likelihood and illustrate its performance in several examples.Comment: JMLR Workshop and Conference Proceedings, 18th International Conference on Artificial Intelligence and Statistics (AISTATS), San Diego, California, USA, 9-12 May 2015 (Vol. 38, pp. 921-929). arXiv admin note: substantial text overlap with arXiv:1207.575

Mechanical Characterization of Fourth Generation Composite Humerus

Mechanical data on upper extremity surrogate bones, supporting use as biomechanical tools, is limited. The objective of this study was to characterize the structural behaviour of the fourth-generation composite humerus under simulated physiologic bending, specifically, stiffness, rigidity, and mid-diaphysial surface strains. Three humeri were tested in four-point bending, in anatomically defined anteroposterior (AP) and mediolateral (ML) planes. Stiffness and rigidity were derived using load–displacement data. Principal strains were determined at the anterior, posterior, medial, and lateral surfaces in the humeral mid-diaphysial transverse plane of one specimen using stacked rosettes. Linear structural behaviour was observed within the test range. Average stiffness and rigidity were greater in the ML (918 ± 18 N/mm; 98.4 ± 1.9 Nm2) than the AP plane (833 ± 16 N/mm; 89.3 ± 1.6 Nm2), with little inter-specimen variability. The ML/AP rigidity ratio was 1.1. Surface principal strains were similar at the anterior (5.41 µε/N) and posterior (5.43 µε/N) gauges for AP bending, and comparatively less for ML bending, i.e. 5.1 and 4.5 µε/N, at the medial and lateral gauges, respectively. This study provides novel strain and stiffness data for the fourth-generation composite humerus and also adds to published construct rigidity data. The presented results support the use of this composite bone as a tool for modelling and experimentation

Diagnostic accuracy of cone-beam computed tomography in detecting secondary caries under composite fillings: An in vitro study

Purpose: The aim of this in vitro study was to assess the diagnostic performance of cone-beam computed tomography (CBCT) in the detection of secondary carious lesions under composite resin fillings applied to different types of cavities. Materials and Methods: Occlusal cavities (O) (n=18), occlusal cavities with mesial or distal component (MO/DO) (n=30), and mesial–occlusal–distal cavities (MOD) (n=30) were prepared in seventy eight extracted human posterior teeth. In half of the cavities in each group, artificial secondary caries lesions were simulated. All cavities were restored by using composite resin. All specimens were embedded in silicone and they were positioned to have approximal contacts. CBCT imaging was done and data were evaluated two times with two week interval by two observers, using a five-point confidence scale. Intra- and inter-observer agreements were calculated with Kappa statistics (κ). The area under (Az) the receiver operating characteristic (ROC) curve was used to evaluate the diagnostic accuracy. Results: Intra- (κ =0.89) and inter-observer (κ = 0.79) agreements were found to be excellent. Az values were highest for the O restorations which is followed by the MOD and DO/MO restorations. Az values for MOD and DO/MO restorations were very low and no statistically significant difference was found. Sensitivity for DO/MO restorations and specificity for MOD restorations were found to be the lowest values. Conclusion: Diagnostic performance of CBCT was higher in O composite restorations than MOD and DO/MO restorations for secondary caries detection. The use of alternative imaging methods rather than CBCT may be useful for evaluating secondary caries under composite MOD and DO/MO restorations