
Component-wise approximate Bayesian computation via Gibbs-like steps
Clarté, Grégoire; Robert, Christian P.; Ryder, Robin; Stoehr, Julien (2021), Component-wise approximate Bayesian computation via Gibbs-like steps, Biometrika, 108, 3, p. 591–607. 10.1093/biomet/asaa090
View/ Open
Type
Article accepté pour publication ou publiéDate
2021Journal name
BiometrikaVolume
108Number
3Publisher
Oxford University Press
Pages
591–607
Publication identifier
Metadata
Show full item recordAuthor(s)
Clarté, GrégoireCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Robert, Christian P.

CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Ryder, Robin
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Stoehr, Julien

CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this dimension grows. To tackle this difficulty, we explore a Gibbs version of the Approximate Bayesian computation approach that runs component-wise approximate Bayesian computation steps aimed at the corresponding conditional posterior distributions, and based on summary statistics of reduced dimensions. While lacking the standard justifications for the Gibbs sampler, the resulting Markov chain is shown to converge in distribution under some partial independence conditions. The associated stationary distribution can further be shown to be close to the true posterior distribution and some hierarchical versions of the proposed mechanism enjoy a closed form limiting distribution. Experiments also demonstrate the gain in efficiency brought by the Gibbs version over the standard solution.Subjects / Keywords
simulation; curse of dimensionality; conditional distributions; convergence of Markov chains; generative model; Gibbs sampler; hierarchical Bayes model; incompatible conditionals; likelihood-free inferenceRelated items
Showing items related by title and author.
-
Clarté, Grégoire; Ryder, Robin J.; Robert, Christian P.; Stoehr, Julien (2019) Document de travail / Working paper
-
Singh, Sumeetpal S.; Sedki, Mohammed; Jasra, Ajay; Pudlo, Pierre; Robert, Christian P.; Lee, Anthony; Marin, Jean-Michel; Kosmidis, Ioannis; Girolami, Mark; Andrieu, Christophe; Cornebise, Julien; Doucet, Arnaud; Barthelme, Simon; Chopin, Nicolas (2012) Article accepté pour publication ou publié
-
Marin, Jean-Michel; Pudlo, Pierre; Robert, Christian P.; Ryder, Robin J. (2012) Article accepté pour publication ou publié
-
Ryder, Robin J. (2015) Article accepté pour publication ou publié
-
Kelly, Luke Joseph; Ryder, Robin J.; Clarté, Grégoire (2022) Article accepté pour publication ou publié