rosenblatt_transform_multivarStudent

Auxiliary function that maps uniform samples in [0, 1]^d to samples from the spectral density
of a Matérn kernel (i.e., a multivariate Student distribution).

internal

Provides tools for conditional and spatially dependent
density estimation using Spatial Logistic Gaussian Processes (SLGPs).
The approach represents probability densities through finite-rank
Gaussian process priors transformed via a spatial logistic density
transformation, enabling flexible non-parametric modeling of
heterogeneous data. Functionality includes density prediction,
quantile and moment estimation, sampling methods, and preprocessing
routines for basis functions. Applications arise in spatial statistics,
machine learning, and uncertainty quantification.
The methodology builds on the framework of Leonard (1978)
<doi:10.1111/j.2517-6161.1978.tb01655.x>, Lenk (1988) <doi:10.1080/01621459.1988.10478625>,
Tokdar (2007) <doi:10.1198/106186007X210206>, Tokdar (2010) <doi:10.1214/10-BA605>,
and is further aligned with recent developments
in Bayesian non-parametric modelling: see Gautier (2023) <https://boristheses.unibe.ch/4377/>,
and Gautier (2025) <doi:10.48550/arXiv.2110.02876>).

Athénaïs Gautier

SLGP

Spatial Logistic Gaussian Process for Field Density Estimation

rosenblatt_transform_multivarStudent function

<dl><dt>x</dt>
<dd>A matrix (or vector) of samples in [0, 1]^d to transform.</dd>
<dt>dimension</dt>
<dd>Integer. The dimension of the input space.</dd>
<dt>MatParam</dt>
<dd>Numeric. The Matérn kernel smoothness parameter (default = 5/2).</dd></dl>

Arguments

Rosenblatt transform to multivariate Student distribution — rosenblatt_transform_multivarStudent

<dl>

<dt>x</dt>
<dd>A matrix (or vector) of samples in [0, 1]^d to transform.</dd>


<dt>dimension</dt>
<dd>Integer. The dimension of the input space.</dd>


<dt>MatParam</dt>
<dd>Numeric. The Matérn kernel smoothness parameter (default = 5/2).</dd>

</dl>

rosenblatt_transform_multivarStudent: Rosenblatt transform to multivariate Student distribution

Description

Usage

Value

Arguments