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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Questions around modelling arrival process of randomly sized groups
I have the following situation:
I'm trying to model groups arriving to some location by some process. I assume the distribution on some interval $T$ is a Gamma-Poisson mixture where $\Lambda \sim ...
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Why do we use only event history for temporal point processes?
I'm trying to understand temporal points processes. In particular, neural TPPs. In all the works I've read, the only features fed into the model are a sequence of event timestamps and marks if they ...
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Limit of Ripley's K function as r goes to infinity?
Considering the Ripley's K function as used in spatial point-process analysis, or the closely related L function, I am wondering what the limit of the function is as r approaches infinity. I am aware ...
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Is there a correction for samples from a (linear) Prophet model when trained on an inhomogenous Poisson point process?
Facebook's Prophet is a popular modelling choice for time series forecasting in production due to many steps being automated (and thus convenient). This can sometimes lead to over-reliance on it when ...
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Spatial point process: Homogeneous vs inhomogeneous K-function
I wonder when would you use a homogeneous K-function instead of a inhomogeneous one and what advantage it has over inhomogeneous K-function? In my opinion I think we should always use inhomogeneous ...
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Confirming the validity of a point process model
I have a question regarding a point process model I generated for a biological point pattern exhibiting repulsion and attraction at different scales. My goal for this model was to generate simulated ...
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Bivariate K function for inhomogeneous spatial point processes
I have some inhomogeneous spatial point patterns of individuals in a cactus population. I also have marks, such as "diseased"x "healthy" individuals, and "adult" x "juvenile". I've already computed ...
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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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Is there any gold standard for modeling irregularly spaced time series?
In field of economics (I think) we have ARIMA and GARCH for regularly spaced time series and Poisson, Hawkes for modeling point processes, so how about attempts for modeling irregularly (unevenly) ...
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Are these two equivalent forms for the likelihood of a Poisson point process?
I have a Poisson point process in a bounded region $W$. I'm trying to calculate the likelihood of observing a particular set of points within $W$. I'm told that there are two equivalent forms of ...
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Statistical test whether data conforms to a spatial point process--gaza bombing locations
I came across this image on twitter, and it made me think about testing a point process hypothesis. Now this is a politically sensitive image, and I don't want to run afoul of any SE posting ...
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Normalizing constant calculation of Strauss Process
Suppose that I have the following Strauss Process up to a proportionality constant
$$p(\mu_{1}, \mu_{2},..., \mu_{K},K)\propto \xi^{K}\prod_{i=1}^{K} I(\mu_{i}\in R) *a^{\sum_{i,j}|\mu_{i}-\mu_{j}|<...
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Analysis of cross correlation between point-processes
I would like an advice on a analysis method I am using, to know if it it statistically sound.
I have measured two point processes $T^1 = t^1_1, t^1_2, \ldots, t^1_n$ and $T^2 = t^2_1, t^2_2, \ldots, t^...
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(Using conditional expectation to calculate) expected value of the product of two dependent random variables
Let $\mathbf{X}$ be Binomial point process in $W = [0, 6] \times [0, 4]$ with $n$ points. Let $A_1 = [0, 2] \times [0, 4]$, $A_2 = [0, 6] \times [0, 2]$, and $A_3 = [2, 6] × [2, 4]$. I want to find $E[...
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Tail of the maximum of a time-varying Poisson-GP marked process
Consider a time-varying version of the Poisson-GP marked process on
the real line as commonly used in Peak Over Threshold (POT) modelling
of a variable $Y$. More precisely we have a given time-varying
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A hard core spatial point process that a vehicle encounters as Poisson arrivals?
Does there exist a point process $X$ in the plane with the following two properties?
$X$ is hard core. Discs of radius $h$ can be centered on the points in $X$ without overlapping.
$X$ is ...
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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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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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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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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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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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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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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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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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Use of Poisson distribution to analyse distribution of individuals in space
Dytham 2010 suggests using the Poisson distribution to establish whether individuals are evenly distributed in space.
Say we end up with a map of individuals in a study site that looks like the ...
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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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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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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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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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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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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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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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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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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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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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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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What is the best test to check if pattern is uniformed?
Out of the following, which tests are best to use on uniformed data to make sure it is indeed dispersed
$\chi^2$
Simple NNA
High/Low clustering (Getis - ord)
KNN (Ripley)
Moran
Monte Carlo
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Residuals plot from ripley K function on spatstat
I am a rookie on R and on spatstat package. I would like some help with the Kres function on spatstat. As is always wise to plot the residuals from any kind of ...
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Edge correction of Ripley's K-function for two 1D point processes?
I am just beginng an investigation involving characterizing the dependence between two 1D stochastic point processes $x$, $y$. The natural approach seems to involve Ripley's K-function:
$$
K(t) = \...
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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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Ripley's K Function and L Function for Point Patterns
The following is a spatial point pattern:
and these are the corresponding Ripley's K function and L function for this data:
How are these functions interpreted?
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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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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 ...