Maximum pseudolikelihood for Gibbs point processes
Source:R/GibbsProcesses.R
GibbsPseudolikelihood.RdThe conditional intensity is \(\log\lambda(u | x) = \log\beta + \theta
V(u | x)\) with the canonical statistic V of the Strauss (count within
r), Geyer (change in \(\sum_i \min(sat, t_r(x_i, x))\)), soft-core
(\(-\sum_j (d_j/\sigma_0)^{-2/\kappa}\), zero intensity once a term falls
below -25; \(\sigma_0\) defaults to the smallest nearest-neighbour
distance) or Diggle-Gratton (\(\sum_j \log((d_j - \delta)/(\rho -
\delta))\), \(-\infty\) inside the hard core) model. The Besag
pseudolikelihood is approximated by the Berman-Turner quadrature (data
points plus the nx by ny grid of tile centres, counting weights) and
maximised by Newton's method on the standardised statistic; this is
spatstat.model::ppm with correction = "none" on that
quadrature scheme.
Usage
GibbsPseudolikelihood(
points,
window,
interaction,
r = NULL,
sat = NULL,
kappa = NULL,
sigma0 = NULL,
delta = NULL,
rho = NULL,
nx = 12L,
ny = 12L,
max_iter = 100L
)Arguments
- points
Event locations (n x 2) inside
window.- window
Rectangle
c(xmin, xmax, ymin, ymax).- interaction
"strauss","geyer","softcore"or"diggle_gratton".- r
Interaction radius (Strauss, Geyer).
- sat
Saturation (Geyer).
- kappa
Soft-core index.
- sigma0
Soft-core scale.
- delta, rho
Diggle-Gratton hard core and range.
- nx, ny
Dummy grid dimensions.
- max_iter
Newton iterations.
Value
List with theta (log beta, interaction coefficient),
se, beta, gamma or sigma, loglik,
n_quadrature.
References
Besag, J. (1977). Some methods of statistical analysis for spatial data. Bulletin of the International Statistical Institute 47, 77-92.
Baddeley, A. and Turner, R. (2000). Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42, 283-322.
Diggle, P. J. and Gratton, R. J. (1984). Monte Carlo methods of inference for implicit statistical models. Journal of the Royal Statistical Society B 46, 193-227.