TY - JOUR
T1 - Thinning spatial point processes into Poisson processes
AU - Møller, Jesper
AU - Schoenberg, Frederic Paik
PY - 2010/6
Y1 - 2010/6
N2 - In this paper we describe methods for randomly thinning certain classes of spatial point processes. In the case of a Markov point process, the proposed method involves a dependent thinning of a spatial birth-and-death process, where clans of ancestors associated with the original points are identified, and where we simulate backwards and forwards in order to obtain the thinned process. In the case of a Cox process, a simple independent thinning technique is proposed. In both cases, the thinning results in a Poisson process if and only if the true Papangelou conditional intensity is used, and, thus, can be used as a graphical exploratory tool for inspecting the goodness-of-fit of a spatial point process model. Several examples, including clustered and inhibitive point processes, are considered.
AB - In this paper we describe methods for randomly thinning certain classes of spatial point processes. In the case of a Markov point process, the proposed method involves a dependent thinning of a spatial birth-and-death process, where clans of ancestors associated with the original points are identified, and where we simulate backwards and forwards in order to obtain the thinned process. In the case of a Cox process, a simple independent thinning technique is proposed. In both cases, the thinning results in a Poisson process if and only if the true Papangelou conditional intensity is used, and, thus, can be used as a graphical exploratory tool for inspecting the goodness-of-fit of a spatial point process model. Several examples, including clustered and inhibitive point processes, are considered.
KW - area-interaction point process
KW - Cox process
KW - dependent and independent thinning
KW - Markov point process
KW - Papangelou conditional intensity
KW - Poisson process
KW - Thomas process
U2 - 10.1239/aap/1275055232
DO - 10.1239/aap/1275055232
M3 - Journal article
SN - 0001-8678
VL - 42
SP - 347
EP - 358
JO - Advances in Applied Probability
JF - Advances in Applied Probability
IS - 2
ER -