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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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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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136 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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26 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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22 views

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 ...
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17 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
47 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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65 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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15 views

Mutual info between discrete and continuous RV with history dependence

I am looking for literature references/measures to compute the mutual information between a continuous variable (time series) and a binary variable (a temporal sequence of 0's/1's). Briefly, a time ...
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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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22 views

Latent Point Process Inference

I need to perform inference on a point process, by which I mean I need a statistical model from which I can (at least) estimate likelihoods. The underlying process appears to have a latent structure, ...
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387 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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464 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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20 views

Calculate L-function envelopes from a fitted model: Lest or Linhom?

I have fitted a model to a point pattern using INLA, and generated 1000 simulated pp from the posterior of this model. I want to use these samples to generate the L-function envelope for my data, and ...
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41 views

Does conditional intensity function of some model must perfectly match with data intensity if model is true?

I consider some emperical dataset characterized by a single parameter - the arrival times of events {$t_0,t_1,t_2,...,t_i$} as is commonly adopted for point processes. The Hawkes model is tested for ...
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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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1answer
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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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47 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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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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42 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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131 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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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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1answer
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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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152 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
422 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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1answer
82 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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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
88 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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1answer
352 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
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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
330 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
190 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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1answer
243 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
82 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
164 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
350 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 ...
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62 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 ...
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1answer
224 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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1answer
69 views

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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correlation measures for near-rotationally symmetric sets in the plane

I have two sets of data points $X, Y \subset \mathbb{R}^2$ what are the correlation measures we can use for such point processes? Here the red points are a rotated copy of the blue points. Yet is ...
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72 views

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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48 views

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 ...
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663 views

Difference between time series prediction vs point process prediction

I am working on a problem of predicting event counts based on user history. This is a classical time series analysis problem, and I used the ARIMA model: (wiki). I also applied a Hawkes point process ...
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Good resource for p-thinning of a point process

Can you please tell me what is a good resource about p-thinning of a point process and then finding the distance between the original and obtained process? Something like the Kullback Leibler distance,...
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61 views

point patterns and line segment patterns

How could I attach points to the line segment pattern using R language Function for example I have point pattern on linear network and I have marked line segment pattern I try to attach points in ...