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Bayesian imaging using Plug Play priors: when Langevin meets Tweedie [article]

Rémi Laumont, Valentin de Bortoli, Andrés Almansa, Julie Delon, Alain Durmus, Marcelo Pereyra
2022 arXiv   pre-print
Since the seminal work of Venkatakrishnan et al. in 2013, Plug & Play (PnP) methods have become ubiquitous in Bayesian imaging.  ...  To address these limitations, this paper develops theory, methods, and provably convergent algorithms for performing Bayesian inference with PnP priors.  ...  with Plug & Play priors.  ... 
arXiv:2103.04715v6 fatcat:4xryxmhvd5gvxa6xujnnp3d5w4

Reservoir modeling and inversion using generative adversarial network priors

Lukas J. Mosser, Olivier Dubrule, Martin Blunt
Using GANs as a probabilistic generative model allows them to be incorporated in a Bayesian inversion workflow.  ...  In both cases, the posterior distribution of the petrophysical property distributions was obtained using approximate Bayesian inference over the latent variables.  ...  Plug-and-play generative networks use an approximate Metropolis-adjusted Langevin algorithm (MALA) (Roberts and Tweedie, 1996) derived from stochastic gradient Langevin dynamics (SGLD) (Welling and  ... 
doi:10.25560/80165 fatcat:g4geuhu2nvfj3dzof4hjlcveke

Bayesian Thinking in Spatial Statistics [chapter]

Lance A. Waller
2005 Handbook of Statistics  
In the sections below we review basic motivations for spatial statistical analysis, review three general categories of data structure and associated inferential questions, and describe Bayesian methods  ...  and Tweedie 1997).  ...  through the use of hierarchical structures that play important roles in the analysis of regional, geostatistical, and point process data.  ... 
doi:10.1016/s0169-7161(05)25020-4 fatcat:bxy4vl2kxrguvaup7men2d7mcy

Particle Markov chain Monte Carlo methods

Christophe Andrieu, Arnaud Doucet, Roman Holenstein
2010 Journal of The Royal Statistical Society Series B-statistical Methodology  
Although asymptotic convergence of Markov chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used  ...  This allows us not only to improve over standard Markov chain Monte Carlo schemes but also to make Bayesian inference feasible for a large class of statistical models where this was not previously so.  ...  In relation to this we are looking forward to seeing applications of PMCMC sampling in the context of approximate Bayesian computations (Cornebise and Peters, and Peters and Cornebise) and general graphical  ... 
doi:10.1111/j.1467-9868.2009.00736.x fatcat:zp2uwuaeefekpntzujiwzvyfc4

Bayesian methods for inverse problems in signal and image processing Specialty: Signal and Image Processing presented by Bayesian methods for large scale inverse problems in signal and image processing President Gersende Fort

Yosra Marnissi, Yosra Marnissi, Nelly Pustelnik, Phd-Advisors, Jean-Christophe Pesquet, Emilie Chouzenoux, Ass Prof
2016 unpublished
Otherwise, when Ψ is a smooth function, one can use a Langevin-based MCMC algorithm.  ...  While the PPXA-TV yields very competitive results, the Plug-and-Play is quite ecient for very low count images (x + < 5) but its eciency highly deteriorates for moderate values of x + .  ... 

Soutenue le par Computing strategies for complex Bayesian models

Cole Doctorale De Dauphine -Ed, Marco Banterle, Christian Robert, Christian Robert, Jean-Michel Marin, Sophie Donnet, Robin Ryder
2016 unpublished
This is again particularly helpful in Bayesian statistics when the target is the posterior distribution.  ...  Testing dependence in the Bayesian Gaussian Copula graphical model There are two major advantages in using the Gaussian Copula graphical model when compared with other non-linear measures of dependence  ...  A natural and conjugate prior for such Λ|G's is the G-Wishart distribution W G (δ, D) , with probability density which reduces to the Wishart distribution when the graph is complete.  ... 

Variational Mixture Models for non-Gaussian observations: Applications to molecular data

Stavroula Gerontogianni, Apollo-University Of Cambridge Repository, Leonardo Bottolo
DNA methylation is a well-studied type of epigenetic change, which results in gene silencing and can be dangerous when occurs at tumour suppressor gene loci.  ...  Metropolis-adjusted Langevin algorithms use Langevin dynamics to propose new states and Metropolis Hastings to accept or reject the proposals (Roberts and Tweedie [118] ).  ...  Now, let us consider of having a Bayesian model with θ the model parameters and y the observed data.  ... 
doi:10.17863/cam.85317 fatcat:urtadf5ysrh5bbr6ls5s43cvmm