Bayesian computation for statistical models with intractable normalizing constants

This paper deals with some computational aspects in the Bayesian analysis of statistical models with intractable normalizing constants. In the presence of intractable normalizing constants in the likelihood function, traditional MCMC methods cannot be applied. We propose an approach to sample from such posterior distributions. The method can be thought as a Bayesian version of the MCMC-MLE approach of Geyer and Thompson (1992). To the best of our knowledge, this is the first general and asymptotically consistent Monte Carlo method for such problems. We illustrate the method with examples from image segmentation and social network modeling. We study as well the asymptotic behavior of the algorithm and obtain a strong law of large numbers for empirical averages.Comment: 20 pages, 4 figures, submitted for publicatio

ABC likelihood-freee methods for model choice in Gibbs random fields

Gibbs random fields (GRF) are polymorphous statistical models that can be used to analyse different types of dependence, in particular for spatially correlated data. However, when those models are faced with the challenge of selecting a dependence structure from many, the use of standard model choice methods is hampered by the unavailability of the normalising constant in the Gibbs likelihood. In particular, from a Bayesian perspective, the computation of the posterior probabilities of the models under competition requires special likelihood-free simulation techniques like the Approximate Bayesian Computation (ABC) algorithm that is intensively used in population genetics. We show in this paper how to implement an ABC algorithm geared towards model choice in the general setting of Gibbs random fields, demonstrating in particular that there exists a sufficient statistic across models. The accuracy of the approximation to the posterior probabilities can be further improved by importance sampling on the distribution of the models. The practical aspects of the method are detailed through two applications, the test of an iid Bernoulli model versus a first-order Markov chain, and the choice of a folding structure for two proteins.Comment: 19 pages, 5 figures, to appear in Bayesian Analysi

Extensive light profile fitting of galaxy-scale strong lenses

We investigate the merits of a massive forward modeling of ground-based optical imaging as a diagnostic for the strong lensing nature of Early-Type Galaxies, in the light of which blurred and faint Einstein rings can hide. We simulate several thousand mock strong lenses under ground- and space-based conditions as arising from the deflection of an exponential disk by a foreground de Vaucouleurs light profile whose lensing potential is described by a Singular Isothermal Ellipsoid. We then fit for the lensed light distribution with sl_fit after having subtracted the foreground light emission off (ideal case) and also after having fitted the deflector's light with galfit. By setting thresholds in the output parameter space, we can decide the lens/not-a-lens status of each system. We finally apply our strategy to a sample of 517 lens candidates present in the CFHTLS data to test the consistency of our selection approach. The efficiency of the fast modeling method at recovering the main lens parameters like Einstein radius, total magnification or total lensed flux, is quite comparable under CFHT and HST conditions when the deflector is perfectly subtracted off (only possible in simulations), fostering a sharp distinction between the good and the bad candidates. Conversely, for a more realistic subtraction, a substantial fraction of the lensed light is absorbed into the deflector's model, which biases the subsequent fitting of the rings and then disturbs the selection process. We quantify completeness and purity of the lens finding method in both cases. This suggests that the main limitation currently resides in the subtraction of the foreground light. Provided further enhancement of the latter, the direct forward modeling of large numbers of galaxy-galaxy strong lenses thus appears tractable and could constitute a competitive lens finder in the next generation of wide-field imaging surveys.Comment: A&A accepted version, minor changes (13 pages, 10 figures

Demographic consequences of agricultural practices on a long-lived avian predator

Includes bibliographical references.2022 Fall.To view the abstract, please see the full text of the document