initialize_basisfun_RFF

Draws parameters for standard RFF approximating a Matérn kernel.

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

initialize_basisfun_RFF function

<dl><dt>dimension</dt>
<dd>Integer. Input (\([\mathbf{x},\,t]\)) dimension.</dd>
<dt>nFreq</dt>
<dd>Integer. Number of frequency vectors to be considered.</dd>
<dt>MatParam</dt>
<dd>Numeric. Matérn smoothness parameter (default = 5/2).</dd>
<dt>lengthscale</dt>
<dd>Numeric vector. Lengthscales used for scaling the input space.</dd></dl>

Arguments

Initialize parameters basis functions based on Random Fourier Features — initialize_basisfun_RFF

<dl>

<dt>dimension</dt>
<dd>Integer. Input (\([\mathbf{x},\,t]\)) dimension.</dd>


<dt>nFreq</dt>
<dd>Integer. Number of frequency vectors to be considered.</dd>


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


<dt>lengthscale</dt>
<dd>Numeric vector. Lengthscales used for scaling the input space.</dd>

</dl>

initialize_basisfun_RFF: Initialize parameters basis functions based on Random Fourier Features

Description

Usage

Value

Arguments