Bayesian inference with rescaled Gaussian process priors
By A. van der Vaart, Harry van Zanten. 2007
95 citations recorded by the source corpus.
We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit rescaled Gaussian process priors yielding posteriors that contract around the true parameter at optimal convergence rates. To derive our results we establish bounds on small deviation probabilities for smooth stationary Gaussian processes.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/788374c1bab5eb73b3a268689b99c17b11f53bed
How researchers see this paper
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In Artificial Intelligence
- Andrew M. Stuart
- Sergios Agapiou
- Stig Larsson
- Judith Rousseau
- Richard Nickl
- Kolyan Ray
- Masoumeh Dashti
- I. Castillo
In Statistics and Probability
- Andrew M. Stuart
- Sergios Agapiou
- Stig Larsson
- Judith Rousseau
- Richard Nickl
- Kolyan Ray
- Masoumeh Dashti
- Mark A. Girolami
Citations in the corpus
- Rates of convergence for the posterior distributions of mixtures of betas and adaptive nonparamatric estimation of the density (2010, background): “Interestingly, van der Vaart and van Zanten [16, 17] also study the impact of scaling factors in nonparametric priors constructed as scaled Gaussian processes, and as in our case, considering a random scaling factor allows for adaptive, minimax concentration rates.”
- Posterior Contraction Rates for the Bayesian Approach to Linear Ill-Posed Inverse Problems (2012, methodology): “Our methods assume a relatively weak relation between the prior covariance, noise covariance and forward operator, allowing for a wide range of applications. c⃝ 2013 Elsevier B.V.”