Can We Trust Bayesian Uncertainty Quantification from Gaussian Process Priors with Squared Exponential Covariance Kernel?
نویسندگان
چکیده
Can We Trust Bayesian Uncertainty Quantification from Gaussian Process Priors with Squared Exponential Covariance Kernel?
منابع مشابه
Bayesian inference with rescaled Gaussian process priors
Abstract: 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 e...
متن کاملVariational Bayesian Multinomial Probit Regression with Gaussian Process Priors
It is well known in the statistics literature that augmenting binary and polychotomous response models with gaussian latent variables enables exact Bayesian analysis viaGibbs sampling from the parameter posterior. By adopting such a data augmentation strategy, dispensing with priors over regression coefficients in favor of gaussian process (GP) priors over functions, and employing variational a...
متن کاملCan We Trust Trust?
In this concluding essay I shall try to reconstruct what seem to me the central questions about trust that the individual contributions presented in this volume raise and partly answer. In the first section, I briefly qualify the claim that there is a degree of rational cooperation that should but does not exist, and I shall give a preliminary indication of the importance of the beliefs we hold...
متن کاملGaussian Process Priors with ARMA Noise Models
We extend the standard covariance function used in the Gaussian Process prior nonparametric modelling approach to include correlated (ARMA) noise models. The improvement in performance is illustrated on some simulation examples of data generated by nonlinear static functions corrupted with additive ARMA noise. 1 Gaussian Process priors In recent years many flexible parametric and semi-parametri...
متن کاملMulti-output separable Gaussian process: Towards an efficient, fully Bayesian paradigm for uncertainty quantification
I. Bilionis et al. / Journal of Computational Physics 241 (2013) 212–239 213 The engineering community and, in particular, the researchers in uncertainty quantification, have been making extensive use of surrogates, even though most times it is not explicitly stated. One example is the so-called stochastic collocation (SC) method (see [1] for a classic illustration) in which the response is mod...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM/ASA Journal on Uncertainty Quantification
سال: 2021
ISSN: ['2166-2525']
DOI: https://doi.org/10.1137/19m1253010