# Questions tagged [point-process]

A point process is a stochastic process in which the data are sets of points ordered in a mathematical space. A common example is the Poisson process, in which points are ordered in time with the interarrival times exponentially distributed.

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### Can any thinning of a Poisson point process be thinned further into a Poisson point process?

Is the following true? Let $\Phi$ be a homogenous Poisson point process of positive intensity. Let $X$ be a thinning of $\Phi$ where $X$ is stationary and has positive intensity. Then $X$ can be ...
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### Can any point process be thinned into a Poisson point process?

Is the following true? For any point process $X$ there exists a procedure $\mathcal{P}$ and a (homogenous) Poisson point process $Y$ with intensity $\lambda > 0$ such that the process of drawing a ...
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### Why do we use only event history for temporal point processes?

I'm trying to understand temporal points processes. In particular, neural TPPs. In all the works I've read, the only features fed into the model are a sequence of event timestamps and marks if they ...
1 vote
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### Limit of Ripley's K function as r goes to infinity?

Considering the Ripley's K function as used in spatial point-process analysis, or the closely related L function, I am wondering what the limit of the function is as r approaches infinity. I am aware ...
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### Uniform distribution versus a Poisson homogeneous process with Ripley's K

I'm testing astropy's RipleysKEstimator. I create a 2-dimensional uniform distribution in [0, 1), and obtain its K value for a radius $r=0.5$. It was my ...
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### How to simulate spatial point patterns that have spatial structure similar to that of given spatial point pattern?

I have some spatial point pattern X distributed in polygon wind and I wonder how can I simulate different point patterns that by their spatial properties (for example, number of points, spatial ...
1 vote
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### Point Pattern Analysis: L-r function

I'm new to pattern analysis. And I got a result of L-r function as below. So, how should I interpret the plot? Does it mean the points are cluster when L-r value is less than 0 and dispersed when the ...
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### trimming window in Foxall G-function and J-function in R spatstat

I am using the Jfox function in spatstat to explore the distance of points in a point pattern to the nearest polygon between a ...
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### Does it make sense to consider ratio of pair correlation functions of two point patterns?

I have two point patterns, one is real data, the other one is simulated data from a model I constructed for the real data. Now I want to see if the second order property of the model matches that of ...
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### How to Simulate Pure-Jump Process associated Marked Point Process in R

Fix $M>0$ and let $(\tau_i,\zeta_i)_{i =1}^{\infty}$ be a marked point process associated to the poisson-random measure $\mu$ on $[0,1]\times [-M,M]^2\times [0,M]\times [-M,M]$ with uniform finite-...
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### Point process model diagnostic: Nearest-Neighbor Distance Distribution or Pair Correlation Function?

I have a point pattern which is clearly inhomogeneous. Furthermore, the inhomogeneity has two components: a large scale effect and a local scale effect. I have constructed a Markov point process model ...
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### How should one simulate a continuously-marked point process by Birth and Death MCMC?

As the question states, I am not sure how I should go about doing that. The main issue is how do I draw a sample from the marked space? The way I am doing things now is as follow: If we are in a ...
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### Lcross Confidence Envelopes - R software

I have performed an Lcross examination in R with the following code: ...
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### Spatial Point Process: Does an inhomogeneous first order intensity function affect the second order dependence?

As the title suggests, I am having a bit of confusion on the effect of first order intensity function. If I have a first order intensity function that says in a certain region the points are much more ...
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### How to compute the expected number of events in the following conditional renewal process?

I have a stochastic point process with event times $\{x_1, x_2, ...\}$ and I want to compute the expected number of events $n(T)$ over the interval $[0,T]$. The point process is generated as follows: ...
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### Distance between point process realizations

Is there a valid distance metric for measuring how similar are the realisations of two point processes? E.g. let's say we simulate two histories $h_1, h_2$ in the time interval $[0, T]$ for two ...
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### Ripley K function value in a specific radius and dataset using R's Kest function

I'm having general trouble with calculating Ripley's K function values. The following is a simple spatial point pattern, where both X and Y range from 0 to 200: Here's its corresponding Ripley K ...
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### Inhomogeneous K-function to indicate need for spatial dependence/interaction term in Poisson point process model

I am mapping and modelling a disease of sheep. I have approx 4200 point locations in my dataset, each of which represents the centroid of a given sheep farm. I have created a K-function difference ...
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### Area interaction model sufficient statistics calculation algorithm

I'm currently trying to write a simulation algorithm in Rcpp for a point process model which requires calculating the sufficient statistics for an Area interaction point process model. It entails a ...
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1 vote
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### Maximum Pseudo-Likelihood estimator for soft-core point process

I am trying to fit a soft-core point process model on a set of point pattern using maximum pseudo-likelihood. I followed the instructions given in this paper by Baddeley and Turner And here is the R-...
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1 vote
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### Unexpected behavior in inhomogeneous Cross K Function (Kcross.inhom) [closed]

I am currently analyzing a point pattern in R using the "spatstat" package. I am comparing two different areas, therefore I made two plots for each area (first two plot-left-area1; second ...
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### Point Pattern Analysis: Assumptions for Hopkins-Skellam Index

I am currently analyzing a point pattern in R using the "spatstat" package. My analyses are primarily exploratory, as I do not have any strong reason to suspect either clustering or regularity, though ...
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### Point process - intensity function vs probability density function

Suppose we have a point process in $\mathbb{R}$ with intensity $\lambda(x)$. Then, for a given compact set ${ S}$ we have $$\Lambda({ S})=\int_{\rm S} \lambda(x) \, dx,$$ where $\Lambda({ S})$ is ...
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