estimate.intensity.pixel: Kernel-based intensity estimation on a space-time grid and...

In SepTest: Tests for First-Order Separability in Spatio-Temporal Point Processes

Kernel-based intensity estimation on a space-time grid and its components, and test statistics for first-order separability

Description

Computes kernel-smoothed estimates of spatial, temporal, separable, and non-separable spatio-temporal intensity functions on a regular space-time grid, together with separability diagnostics used in first-order separability analysis.

Usage

estimate.intensity.pixel(X, s.region, t.region, n.grid, edge, owin = NULL)

Arguments

X	Numeric matrix/data.frame with three columns (x, y, t) giving observed events.
s.region	Numeric matrix with two columns defining the spatial window (typically polygon vertices). Grid limits are taken as range(s.region[,1]) and range(s.region[,2]).
t.region	Numeric vector of length 2 giving the temporal window c(tmin, tmax).
n.grid	Integer vector of length 3 giving grid resolution in x, y, and t.
edge	List with components bw (length 3), space (length nrow(X)), and time (length nrow(X)).
owin	Optional observation window of class "owin" (from spatstat.geom). If provided, intensity estimates outside the window are set to NA.

Details

The estimator uses product Gaussian kernels with supplied bandwidths and (Gaussian) edge-correction factors, typically produced by calc.bandwidths.and.edgecorr.

Value

A list with grid coordinates x,y,t, intensity estimates, the diagnostic S.fun, its marginal summaries S.space and S.time, and deviation measures.

References

Ghorbani, M., Vafaei, N., Dvořák, J., and Myllymäki, M. (2021). Testing the first-order separability hypothesis for spatio-temporal point patterns. Computational Statistics & Data Analysis, 161, 107245.

See Also

S.based.functions, calc.bandwidths.and.edgecorr

Examples

n <- 100
X <- cbind(x = stats::runif(n), y = stats::runif(n), t = stats::runif(n, 0, 10))
s.region <- matrix(c(0,0, 1,0, 1,1, 0,1), ncol=2, byrow=TRUE)
t.region <- c(0, 10)
n.grid <- c(10, 10, 5)
edge <- list(bw = c(0.05, 0.05, 0.5), space = rep(1, n), time = rep(1, n))
res <- estimate.intensity.pixel(X, s.region, t.region, n.grid, edge)
str(res)

SepTest documentation built on Feb. 3, 2026, 5:07 p.m.