A J-function for Inhomogeneous Spatio-temporal Point Processes

• We propose a new summary statistic for inhomogeneous intensity-reweighted moment stationarity spatio-temporal point processes. The statistic is defined in terms of the n-point correlation functions of the point process, and it generalizes the J-function when stationarity is assumed. We show that our statistic can be represented in terms of the generating functional and that it is related to the spatio-temporal K-function. We further discuss its explicit form under some specific model assumptions and derive ratio-unbiased estimators. We finally illustrate the use of our statistic in practice.

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

inhomogeneous spatio-temporal point process

intensity-reweighted moment stationarity

J-function

K-function

location-dependent thinning of hard core model

log-Gaussian Cox process

n-point correlation function

Papangelou conditional intensity

Poisson process

(reduced Palm measure) generating functional

Mathematical Statistics

matematisk statistik

Publication and Content Type

ref (subject category)

art (subject category)