initialize_basisfun_inducingpt

Computes kernel matrix and its decompositions for use in inducing-point basis functions.

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_inducingpt function

<dl><dt>dimension</dt>
<dd>Integer. Input (\([\mathbf{x},\,t]\)) dimension.</dd>
<dt>kernel</dt>
<dd>Character. Kernel type ("Exp", "Mat32", "Mat52", "Gaussian").</dd>
<dt>lengthscale</dt>
<dd>Numeric vector. Lengthscales used for scaling the input space.</dd>
<dt>pointscoord</dt>
<dd>Optional matrix of inducing point coordinates.
If none is provided, we sample them uniformly in the unit hypercube.</dd>
<dt>numberPoints</dt>
<dd>Integer. Number of inducing points
(used if <code>pointscoord</code> is NULL).</dd></dl>

Arguments

Initialize parameters for inducing-point basis functions — initialize_basisfun_inducingpt

<dl>

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


<dt>kernel</dt>
<dd>Character. Kernel type ("Exp", "Mat32", "Mat52", "Gaussian").</dd>


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


<dt>pointscoord</dt>
<dd>Optional matrix of inducing point coordinates.
If none is provided, we sample them uniformly in the unit hypercube.</dd>


<dt>numberPoints</dt>
<dd>Integer. Number of inducing points
(used if <code>pointscoord</code> is NULL).</dd>

</dl>

initialize_basisfun_inducingpt: Initialize parameters for inducing-point basis functions

Description

Usage

Value

Arguments