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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What is the difference between a hazard rate and a recurrence rate in a renewal process?

I do not see any difference between a hazard rate and a recurrence rate for a renewal process. Is there one? Here is my (possibly incorrect) understanding: If a point process has time-varying rate ...
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Computing discrete survivor functions

I am trying to understand the survivor function for a discrete point process, but I am finding two conflicting definitions. Any clarification would be much appreciated. For illustration purposes, ...
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Diversity enhancing sampling from positively dependent random measures

Is there any efficient method to maximize diversity of samples when sampling from a set of positively dependent random variables?
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28 views

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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Prediction error of interpolation using Gaussian kernel smoothed intensity

I'll like to know how to calculate the prediction error (or interpolation error) between Gaussian kernel smoothed intensity images created if I comparing all data set (census) with a sample of the ...
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1answer
30 views

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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28 views

Combinatorial Dimension of Statistical Models for Point Process Data

What measure of combinatorial complexity can be used for models fitted on point process data (e.g. Hawkes or Poisson processes)? Is VC dimension or some generalization of it (e.g. Pollard's pseudo-...
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1answer
23 views

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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1answer
39 views

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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1answer
116 views

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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22 views

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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1answer
83 views

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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26 views

Lcross Confidence Envelopes - R software

I have performed an Lcross examination in R with the following code: ...
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176 views

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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25 views

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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1answer
247 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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58 views

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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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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1answer
50 views

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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159 views

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-...
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156 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 ...
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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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908 views

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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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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37 views

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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49 views

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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35 views

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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219 views

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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51 views

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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175 views

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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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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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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125 views

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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181 views

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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1answer
524 views

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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99 views

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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133 views

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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1answer
104 views

All-to-All distances for point pattern analysis

I am new to point pattern analysis. Trough my readings I haven't seen that any book would suggest to use All-to-All distances for point pattern analysis, but rather they talk about NND or other ...
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483 views

Stationarity assumption for a point process

as I understand stationarity of a point process implies that it is invariant under translation. Imagine one has numerous realizations of the same point process. Due to the nature of this process, it ...
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1answer
118 views

Analysis of spatial replicated patterns

I am new to spatstat. I have a set of replicated patterns, I perform L test for each pattern and I pool the resulting statistic (using pool statistics in spatstat). Now I would like to perform a ...
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1answer
414 views

Averaging Ripley's K or L function for several samples

Would much appreciate to hear your opinion about the following strategy: I have several samples of point patterns, witch are results from somw replicated experiment. The number of points and area of ...
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2answers
257 views

How to test change in rate of event occurrences?

Let x be the times (in whatever unit) at which a given event has been observed. ...
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280 views

Time Rescaling Theorem and Residual Analysis

Let $\mathcal{P}$ an homogeneous unit rate Poisson process. It's conditional intensity function (star indicating conditioning on the history) can be written as $$\lambda^*(t) = \lambda = 1$$ meaning ...
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1answer
94 views

Generating pattern of points from a pairwise interaction space point process

I have estimated the parameters of a non-homogeneous poisson space point process using Metropolis+gibbs from some observation data. I know: $N$: Number of points inside my observation window $\...
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1answer
191 views

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 ...
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1answer
451 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 ...