# 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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### 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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1 vote
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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 ... 24 views

### 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 ...
1 vote
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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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1 vote
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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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1 vote
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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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1 vote
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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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1 vote
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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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