estimate.intensity.point

Computes kernel-based spatial, temporal, separable, and non-separable intensity
estimates evaluated at the observed spatio-temporal event locations. The function
also returns the separability diagnostic \(S_i\) and global deviation measures
quantifying departures from first-order separability.

Provides statistical tools for testing first-order separability in spatio-temporal point processes, that is, assessing whether the spatio-temporal intensity function can be expressed as the product of spatial and temporal components. The package implements several hypothesis tests, including exact and asymptotic methods for Poisson and non-Poisson processes. Methods include global envelope tests, chi-squared type statistics, and a novel
Hilbert-Schmidt independence criterion (HSIC) test, all with both block and pure permutation procedures. Simulation studies and real world examples, including the 2001 UK foot and mouth disease outbreak data, illustrate the utility of the proposed methods. The package contains all simulation studies and applications presented in Ghorbani et al. (2021) <doi:10.1016/j.csda.2021.107245> and Ghorbani et al. (2025) <doi:10.1007/s11749-025-00972-y>.

Mohammad Ghorbani

SepTest

Tests for First-Order Separability in Spatio-Temporal Point
Processes

Nafiseh Vafaei

estimate.intensity.point function

<dl><dt>X</dt>
<dd>Numeric matrix/data.frame with three columns <code>(x,y,t)</code> giving event coordinates.</dd>
<dt>n.grid</dt>
<dd>Integer. Included for API compatibility with grid-based routines; not used.</dd>
<dt>edge</dt>
<dd>List with components <code>bw</code> (length 3), <code>space</code>, and <code>time</code>.
<code>space</code> and <code>time</code> are Gaussian edge-correction masses evaluated at each event;
each may be a scalar or a numeric vector of length <code>nrow(X)</code>.</dd></dl>

Arguments

Kernel intensity estimates of a spatio-temporal point process at observed points and its components,
and test statistics for first-order separability — estimate.intensity.point

<dl>

<dt>X</dt>
<dd>Numeric matrix/data.frame with three columns <code>(x,y,t)</code> giving event coordinates.</dd>


<dt>n.grid</dt>
<dd>Integer. Included for API compatibility with grid-based routines; not used.</dd>


<dt>edge</dt>
<dd>List with components <code>bw</code> (length 3), <code>space</code>, and <code>time</code>.
<code>space</code> and <code>time</code> are Gaussian edge-correction masses evaluated at each event;
each may be a scalar or a numeric vector of length <code>nrow(X)</code>.</dd>

</dl>

estimate.intensity.point: Kernel intensity estimates of a spatio-temporal point process at observed points and its components, and test statistics for first-order separability

Description

Usage

Value

Arguments

Details

See Also

Examples