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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Likelihood for a log Gaussian Cox process (LGCP)
Suppose I have a log Gaussian Cox process (LGCP) $X$ with log intensity function $\lambda(x)=S(x)$ where $S$ follows a Gaussian process. Since LGCP still falls under the umbrella of inhomogeneous ...
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Penalize an attribute of points based on their distance from a line without use of any threshold
We have a set of points and a line. Each point in the set has a weight attribute that is an integer. How we could penalize this weight based on the distance of the point from the line without using ...
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Simulation envelopes for Foxall J not containing the line y=1 (fully reproducible example)
During some exploratory analysis of my data I noticed that when Jfox was calculated for a point pattern relative to some polygons, I frequently obtained that the pooled envelopes area did not include ...
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Convergence of intensity function of self-exciting point processes imply convergence of processes?
For every $n \in \mathbb{N}$, let $N_n$ be the point process on $[0,1]$ defined by the conditional intensity function $\lambda_n: [0,1] \rightarrow \mathbb{R_{\geq 0}}$, where
$$ \lambda_n(t) = \mu_n(...
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Simulating a Strauss Point Process with Birth-Death Algorithm
Suppose that I have the following two unconditional Strauss Process
$$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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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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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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