initialize_basisfun

Initializes the parameter list needed for a basis function.

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 function

<dl><dt>basisFunctionsUsed</dt>
<dd>Character. The type of basis function to use.
One of: "inducing points", "RFF", "Discrete FF", "filling FF", "custom cosines".</dd>
<dt>dimension</dt>
<dd>Integer. Dimension of the input space $[\mathbf{x},\,t]$.</dd>
<dt>lengthscale</dt>
<dd>Numeric vector. Lengthscales used for scaling the input space.</dd>
<dt>opts_BasisFun</dt>
<dd>List. Optional. Additional options specific to the chosen basis function.
If the type is "custom cosines", the basis functions considered are $ coef\cos(freq^\top [x, t] + offset) $
and the user must provide three vectors: <code>opts_BasisFun$freq</code>, <code>opts_BasisFun$offset</code> and <code>opts_BasisFun$coef</code>.
Users can refer to the documentation of specific basis function initialization functions
(e.g., <code>initialize_basisfun_inducingpt</code>, <code>initialize_basisfun_RFF</code>,
<code>initialize_basisfun_fillingRFF</code>, <code>initialize_basisfun_discreteFF</code>, etc.) for details on the available options.</dd></dl>

Arguments

Initialize basis function parameters — initialize_basisfun

<dl>

<dt>basisFunctionsUsed</dt>
<dd>Character. The type of basis function to use.
One of: "inducing points", "RFF", "Discrete FF", "filling FF", "custom cosines".</dd>


<dt>dimension</dt>
<dd>Integer. Dimension of the input space $[\mathbf{x},\,t]$.</dd>


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


<dt>opts_BasisFun</dt>
<dd>List. Optional. Additional options specific to the chosen basis function.
If the type is "custom cosines", the basis functions considered are $ coef\cos(freq^\top [x, t] + offset) $
and the user must provide three vectors: <code>opts_BasisFun$freq</code>, <code>opts_BasisFun$offset</code> and <code>opts_BasisFun$coef</code>.
Users can refer to the documentation of specific basis function initialization functions
(e.g., <code>initialize_basisfun_inducingpt</code>, <code>initialize_basisfun_RFF</code>,
<code>initialize_basisfun_fillingRFF</code>, <code>initialize_basisfun_discreteFF</code>, etc.) for details on the available options.</dd>

</dl>

initialize_basisfun: Initialize basis function parameters

Description

Usage

Value

Arguments