# 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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### 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 does a covariance intensity function measure clustering?

I was taught in a class on spatial statistics that the covariance intensity function (defined below) measured clustering and inhibition in a point process, but isn't used because good test statistics ...
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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: ...
49 views

### 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 ...
179 views

### 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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### Simplest model for simulation of inter-arrival times with long-memory

I'm trying to model the inter-arrival times of stochastic point process that I've observed for the purpose of simulating it. The Autocorrelation Function (ACF) of the inter-arrival times shows ...
19 views

### 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 two plots-...
134 views

### 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 ...
818 views

### 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 ...
39 views

### 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 ...
38 views

### 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 ...
43 views

### 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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### Hawkes-Process for non binary events

I am currently using a univariate Hawkes-process for modeling the behaviour of agents in a social network. For example, the likelihood that a user will tweet in the next period is defined by the ...
410 views

### p-value for complete spatial randomness tests

I am using the Kolmogorov-Smirnov test to study the homogeneity of a point pattern in 3D using the distance transform to a structure as a covariate. I am using the spatstat book, where it is ...
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### Marked point process with spatial correlation (hard spheres with varying radii)

Problem: Given an arrangement of spheres of varying radii in a fixed domain , I am trying to simulate an arrangement of spheres in a domain of arbitrary size having the same statistics. The radii of ...
67 views

### The pdf of last interval of a Poisson process in $[0,T]$

Assume a Poisson point process with rate $\lambda$ in time $[0,T]$. Supoose $X$ is the random variable representing the time between the last arrival and $T$. What is the probability density function ...
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### Sum of squared error and point process data

One standard distance measure applied in continuous data analysis is average sum of squared error. However, this method cannot be applied for point process data. And there is an alternative solution ...
250 views

### spatio-temporal density analysis of point patterns with lgcp

I am trying to use the R package lgcp to estimate density based on a point pattern over time. I follow the example given by the authors of the package in this article, but even the first step (copied ...
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### Can data clustering algorithms be used to find the borders of an area in 2D space ?

If we have spatial points randomly distributed in 2D space, then we clustered those points according to some parameters, say location x,y. Can we use the same clustering algorithm and apply it on ...
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### poisson regression and discretization

I have data which is a natural fit for Poisson regression but I'm not sure how to correctly discretize the data into bins in a canonical or "best" way. One intuition is that I should use "small" ...
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### Beeping boxes: survival analysis? times series?

I'm currently at a loss. I want to make a model that predicts when content providers aren't going to update anymore, but I'm having trouble finding a model that allows me to capture what I want. To ...