Multitype Point Process Analysis of Spines on the Dendrite Network of a Neuron

Abstract

Summary We develop methods for analysing the spatial pattern of events, classified into several types, that occur on a network of lines. The motivation is the study of small protrusions called ‘spines’ which occur on the dendrite network of a neuron. The spatially varying density of spines is modelled by using relative distributions and regression trees. Spatial correlations are investigated by using counterparts of the K‐function and pair correlation function, where the main problem is to compensate for the network geometry. This application illustrates the need for careful analysis of spatial variation in the intensity of points, before assessing any evidence of clustering.

Point process models for presence‐only analysis

“…For example, when modelling roadkill events (Ramp et al 2005), presence points occur along a road network. Poisson PPMs can be fitted to point events arising along networks relatively easily; however, methods for studying and accounting for dependence in point events along networks are a little explored topic (Baddeley, Jammalamadaka & Nair 2014).…”

Regularized estimation for highly multivariate log Gaussian Cox processes

“…Research on statistical methodology for multivariate point patterns has mainly considered bivariate or trivariate point patterns. Some exceptions are Diggle et al [2005] and Baddeley et al [2014] who considered four-and six-variate multivariate Poisson processes and more recently Jalilian et al [2015] and Waagepetersen et al [2016] who considered five-and nine-variate multivariate Cox processes. A truly high-dimensional analysis was conducted by Rajala et al [2018] who introduced a multivariate Gibbs point process and applied it to a point pattern data set containing locations of 83 species of rain forest trees.…”

Kernel Density Estimation on a Linear Network

“…The ‘lines’ that form the network may be roads, rivers, rail lines, electrical wires, nerve fibers, airline routes or soil cracks. The ‘points’ may be traffic accidents, vehicle thefts or street crimes (Yamada & Thill, ; Lu & Chen, ; Xie & Yan, ; Ang et al, ); roadside trees or invasive species (Spooner et al, ; Deckers et al, ); retail stores, roadside kiosks or urban parks (Okabe & Kitamura, ; Okabe & Okunuki, ; Okunuki & Okabe, ; Comber et al, ); insect nests (Voss et al, ; Ang et al, ); neuroanatomical features (Yadav et al, ; Jammalamadaka et al, ; Baddeley et al, ); or sample points along a stream (Ver Hoef et al, ; Ver Hoef & Peterson, ; Som et al, ). For example, Fig.…”

“…More progress has been made in the special case of a network without loops. Applications include river and stream networks (Cressie & Majure, 1997;Ver Hoef et al, 2006;Cressie et al, 2006;Ver Hoef & Peterson, 2010;O'Donnell et al, 2014) and the dendrites of neurons (Baddeley et al, 2014). On such networks, there is a unique shortest path between any two points that are connected, and this makes it possible to perform non-parametric regression on the network in a simple way.…”