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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Simulating a Strauss Point Process with Birth-Death Algorithm

Suppose that I have the following two unconditional Strauss Process $$f_{1}(x_{1}, x_{2},..., x_{n};a,\delta) \propto \prod_{i}^{n}\phi(x_{i}) \prod_{1\leq i \leq j \leq n}a^{\left | x_{i}-x_{j} \...
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pointwise envelopes not including Theoretical line Foxall J

I am computing pointwise envelopes for the Foxall's J function to investigate the whether some point patterns of interest are clustered, avoid or are independent from other point patterns or polygons. ...
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Algorithm for generating a Poisson process on a complicated 2d geometry

I am looking at some count data by geographic counties in California. As a starting point, a Poisson process came to mind--though there are other good choices like negative binomial, etc. Given a $\...
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Definition of point processes

We say a finite point process $X$ on $[N]=\{1,…,N\}$ can be understood as a random subset. It is defined either via its inclusion probabilities, that is $\mathbb{P}(S \subseteq X)$ for $S \subseteq [N]...
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Is the following definition of the variance of the number of points correct?

I have been asked to calculate "the variance of the number of points" in the following pictures, inside the circles: I was looking for the definition of "the variance of the number of ...
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Doing a temporal cluster analysis for terrorism

I am trying to conduct a temporal cluster analysis on a terrorism dataset, but I've hit a bit of a brick wall regarding the method. The dataset spans between 01-01-2015 and 31-12-2019, and for my 3 ...
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Knowing when to stop with spatial point thinning -- is an approach with Clark-Evans test valid?

I need a random sample of presence points from the species' area to use in distribution modeling. I have an excessive amount of spatially clustered presence records, so I use minimum nearest neighbor ...
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Is Nearest Neighbor Distance Ratio (NNDR) test good for assessing point pattern?

Regularity of point pattern is routinely checked in ArcGIS with the Nearest Neighbor Distance Ratio test providing significance estimations: https://pro.arcgis.com/en/pro-app/latest/tool-reference/...
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Best models to relate a frequent point process and a rare point process

I want to relate two processes and understand their cause-and-effect relationship. The first process is a point process with frequent occurrences (more than 90%) and has support [0,1] and truncated ...
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Predict background counts given past observations and assumption of linear variation of the rate parameter in time

Consider the following problem. We have a time series of counts (poisson-distributed) data. In this time series we can select an off-pulse window in which only background is present and a subsequent ...
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Simple point processes and the expected value

When considering simple point processes, how is $$P(t_{n+1} \in [t;t+dt]) = E[N([t;t+dt])]$$, where $N(A)$ is the number of points in interval $A$ and $dt$ is the length of an infinitesimal interval. ...
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KS Test for Hawkes Process

I am analyzing some data by applying 1d-Hawkes processes. To evaluate the fit of the model itself (and particularly the chosen kernel, i.e. exponential), I am performing a KS test. However, it is not ...
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spatstat::plot.envelope observed line longer than significance band [duplicate]

Using the R package spatstat I'm plotting pooled pointwise envelopes of the function Jfox calculated for different point pattern in an hyperframe. The workflow is ...
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spatstat::plot.envelope observed line longer than shading

Using the R package spatstat I'm plotting pooled pointwise envelopes of the function Jfox calculated for different point pattern in an hyperframe. The workflow is ...
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1 answer
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What is the "sensible default" for the Kest function of the spatstat package?

I'm reading the documentation on the Kest function (page 731) from the spatstat package. For the argument $r$, that is the "Vector of values for the argument $...
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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 ...
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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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1 answer
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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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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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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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Fit Hawkes process to 1d data using python package TICK

How can one fit the 1-dimensional Hawkes process with exponential kernel to the experimental 1d dataset (t1,t2,t3...tn) and check the goodness-of-fit via tick python3 package? I found on official ...
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Machine Learning on Sequential Data Reperesenting Events

Would you please recommend which model should I use for modeling user activity observing certain events that happen to them in time. I want to make sense of the history of events (just a presence of ...
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Inconsistency of kernel intensity estimator

I have read that the kernel intensity estimator of a point process is not consistent, because the variance at any point is "of order 1". What does he mean by "of order 1"? I would like to understand ...
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Create points pattern in R using spatstat package with specified number of points

Is it possible to generate points pattern with Poisson and Thomas process in R using spatstat package with specified number of points? I had genereted Strauss point pattern using the Metropolis-...
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How to evaluate global and local effects in one model

I want to test the effect of elevation on the intensity of burrowing by gopher tortoises in flatwoods [a type of pine savanna characterized by both low (wet) and high (dry) areas]. However, in several ...
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Resource on Point Processes

I am not sure if this is the right place to ask and I'm new here. I'm a Ph.D. student (electronics engineering) studying mainly on (multi) target tracking. The common approach is to use a Bayesian ...
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Is the Matérn covariance function associated with the Matérn cluster process?

This question follows on from something I couldn't figure out in this question. Is there a relationship between the Matérn cluster process and Matérn covariance function beyond both being ...
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The probability of disc that fully overlaps discs in a Boolean model

In a example of Boolean model, points are scattered in the plane according to a homogeneous Poisson process of intensity $λ$. On each of these points a disc of fixed radius $r$ is placed. Similar to ...
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Mean of nearest neighbour distance in a clustered distribution

What would be the expected value of distances to the nearest neighbor in a set of points in 2-dim space that have a clustered (not random) spatial distribution? If the distribution is random the ...
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ETAS model initial parameter determining

I am trying to fit a spatio-temporal epidemic type after schock model to an Earthquake catologue using ETAS package R. However, I do not know about it too much. Without good initial parameter set the ...
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Point process weakly modulated by an external signal

I would like to modulate the probability of firing of a point process by an external signal $x_{ext}(t) $, of varying amplitude and a specific frequency range (filtered Gaussian noise). The mean rate $...
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Hawkes processes: interpretation of maximum likelihood estimates disagreeing with moment estimator estimates?

So, I have some data.. and a parameterized Hawkes process which I estimate parameters for via maximum likelihood... the residuals ( the compensator aka the dual-predictable projection) are good in ...
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Distribution of distance to nearest (farthest) neighbour in normal data cloud

Here is an example of standard normal datasets (spherical, i.e. identity covariance matrices) in 1, 2, 3, 5, 10 dimensions, n=100 points. The picture shows observed ...
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Mean Nearest Neighbor test vs Nearest Neighbor function envelope test?

I am analyzing a point pattern using G (nearest neighbor cumulative distribution) function, followed up by the envelope tests and in the same time using Nearest Neighbor Index test (Clark Evans test )...
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Test for summary funtions: KS or envelope tests?

I want to study a point pattern using cumulative NND (Nearest Neighbor Distance) "G" function . The main task is to test H0: the point process is compatible with a null model (can be CSR (complete ...
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Extracting intervals out of an unevenly spaced time series

I am having a list of unevenly spaced data points - just occurrences, no values - and want to split them into intervals grouping occurrences, which are close together like so: Currently I am ...
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