Efficient sampling of non log-concave posterior distributions with mixture of noises

Abstract

This paper focuses on a challenging class of inverse problems that is often encountered in applications. The forward model is a complex non-linear black-box, potentially non-injective, whose outputs cover multiple decades in amplitude. Observations are supposed to be simultaneously damaged by additive and multiplicative noises and censorship. As needed in many applications, the aim of this work is to provide uncertainty quantification on top of parameter estimates. The resulting log-likelihood is intractable and potentially non-log-concave. An adapted Bayesian approach is proposed to provide credibility intervals along with point estimates. An MCMC algorithm is proposed to deal with the multimodal posterior distribution, even in a situation where there is no global Lipschitz constant (or it is very large). It combines two kernels, namely an improved version of (Preconditioned Metropolis Adjusted Langevin) PMALA and a Multiple Try Metropolis (MTM) kernel. Whenever smooth, its gradient admits a Lipschitz constant too large to be exploited in the inference process. This sampler addresses all the challenges induced by the complex form of the likelihood. The proposed method is illustrated on classical test multimodal distributions as well as on a challenging and realistic inverse problem in astronomy.

References in corpus (12)

• Estimating Mutual Information
• A model for atomic and molecular interstellar gas: The Meudon PDR code
• The anatomy of the Orion B Giant Molecular Cloud: A local template for studies of nearby galaxies
• A Survey of Monte Carlo Methods for Parameter Estimation
• Equi-energy sampler with applications in statistical inference and statistical mechanics
• A Survey of Stochastic Simulation and Optimization Methods in Signal Processing
• Structure of photodissociation fronts in star-forming regions revealed by observations of high-J CO emission lines with Herschel
• Cosmic Emulation: Fast Predictions for the Galaxy Power Spectrum
• A Review of Multiple Try MCMC algorithms for Signal Processing
• Langevin diffusions and the Metropolis-adjusted Langevin algorithm
• On the flexibility of the design of Multiple Try Metropolis schemes
• Constraining physical conditions for the PDR of Trumpler 14 in the Carina Nebula

Cited by in corpus (2)

• Beetroots: spatially-regularized Bayesian inference of physical parameter maps -- Application to Orion
• Estimating the dense gas mass of molecular clouds using spatially unresolved 3 mm line observations