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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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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Log Gaussian Cox Process with multi-scale cluster (non-stationary covaraince structure)
As the title suggests, I am working on point patterns that exhibit highly varying sizes of clusters. This kind of data arises mostly in astronomy where 3d point patterns are projected onto 2d space, ...
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Can random effects be used in the spatial LGCP package (from JSS paper by Taylor et al. 2015)?
I am reading the excellent statistical software paper found here in this link. The paper is an R implementation of Log-Gaussian Cox processes for spatial point process applications.
Whilst the ...
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34 views
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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2answers
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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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17 views
How to measure the effects of multiple shorter time-series on one longer time-series?
I have a question pertains to time-series analysis.
For example, I have a time-series data about the downloads of an app for a month. And I want to know that the effects on the downloads time-series ...
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40 views
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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43 views
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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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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12 views
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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15 views
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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84 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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48 views
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
37 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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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
32 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
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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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124 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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1answer
86 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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34 views
Lcross Confidence Envelopes - R software
I have performed an Lcross examination in R with the following code:
...
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247 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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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
458 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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22 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
56 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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188 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 ...
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220 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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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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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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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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264 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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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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1answer
188 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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0answers
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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
137 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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192 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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559 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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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
108 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 ...
