English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In nonparameteric Bayesian approaches, Gaussian stochastic processes canserve as priors on real-valued function spaces. Existing literature on theposterior convergence rates under Gaussian process priors shows that it ispossible to achieve optimal or near-optimal posterior contraction rates if thesmoothness of the Gaussian process matches that of the target function. Amongthose priors, Gaussian processes with a parametric Mat\'ern covariance functionis particularly notable in that its degree of smoothness can be determined by adedicated smoothness parameter. Ma and Bhadra(2023) recently introduced a newfamily of covariance functions called the Confluent Hypergeometric (CH) classthat simultaneously possess two parameters: one controls the tail index of thepolynomially decaying covariance function, and the other parameter controls thedegree of mean-squared smoothness analogous to the Mat\'ern class. In thispaper, we show that with proper choice of rescaling parameters in the Mat\'ernand CH covariance functions, it is possible to obtain the minimax optimalposterior contraction rate for $\eta$-regular functions. Unlike the previousresults for unrescaled cases, the smoothness parameter of the covariancefunction need not equal $\eta$ for achieving the optimal minimax rate, foreither rescaled Mat\'ern or rescaled CH covariances, illustrating a key benefitfor rescaling. The theoretical properties of the rescaled Mat\'ern and CHclasses are further verified via extensive simulations and an illustration on ageospatial data set is presented.

Posterior Concentration for Gaussian Process Priors under Rescaled Mat\'ern and Confluent Hypergeometric Covariance Functions