The point-process tag has no wiki summary.
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1answer
39 views
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?
4
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1answer
98 views
Are there models for “censored” spatial point processes?
This is a problem I'm encountering in the context of analyzing a data set comprised of all crime locations in a city over a fixed time interval, although it could potentially arise in other types of ...
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3answers
463 views
Measure the uniformity of distribution of points in a 2D square
I have a 2D square, and I have a set of points inside it, say, 1000 points. I need a way to see if the distribution of points inside the square are spread out (or more or less uniformly distributed) ...
3
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1answer
77 views
Interpretation of spatial Gcross plots
On page 192 of Analysing spatial point patterns in 'R' (Baddeley 2011), there are plots of the Gcross function for the amacrine dataset. I am looking for an interpretation of the plot. off/off and ...
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0answers
121 views
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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5answers
631 views
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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0answers
41 views
Learning models for dependent point processes
This is largely a literature request.
I have some data consisting of, for each use of a credit card, the card owner, the store, and the time of the use. This could be viewed as a collection of ...
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0answers
67 views
Markov point processes and mobility
I want to model the case where a particular message is forwarded from a source to multiple nodes with transmission radius r (in multiple hops), until the message reaches a particular destination. The ...
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0answers
87 views
How to estimate the intensity of a multidimensional point process?
Note that for a homogeneous point process the density is just a number, while for an in-homogeneous process it is a function. In addition, how can I distribute that function on a larger study region ...
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2answers
105 views
Edge effects in K-function
I am trying to write some codes for distance-based evaluation of point process such as $G$, $F$ and $K$ functions. In the implementation of $K$ there is a case to consider edge effect to have an ...
3
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2answers
279 views
What are similarity measures between a line and a set of points?
A colleague discussed about a concept of similarity between two different entities line and a set of points. My first guess for solution was considering distances squared ($d^2$) as in LS. So for the ...
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1answer
145 views
What is conditioning in spatial statistics?
Could someone explain to me:
the concept of "conditioning" in spatial statistics in a fairly advanced context?
Here is an example to clarify the question:
Step 1) generate a 2D point process, here 6 ...
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0answers
135 views
Dependent thinning poisson process
If $N_1$ and $N_2$ are independent Poisson processes then the superposition is a Poisson process. Is is possible to construct two dependent Poisson processes such that the superposition is a Poisson ...
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1answer
73 views
Attractive pairwise interaction point process
I'm doing some spatial pattern analysis. After looking over some work on Markov Point Processes, I'm finding that all of the pairwise interaction processes are 'repulsive'.
In "Statistical Inference ...
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0answers
119 views
How to condition a marked point processes?
Conditioning a point process is the concept being investigated in this post. The marked point processes are of interest.
Figure A demonstrates a phenomenon being investigated for modelling. We ...
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1answer
219 views
Mixing and dividing point processes
At the following figure at left side two realizations of point processes with different density (intensity) $\lambda_1$ and $\lambda_2$ is being mixed matching the center of the belonging areas to ...
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1answer
628 views
What are density and intensity of point pattern?
A simplified explanation with the focus on the following questions is being inquired. Appreciation goes in advance to whom provides scientific--simple--practical explanation.
Having an area A ...
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0answers
126 views
How to condition a point process to the actual sampling data?
Figure A demonstrates a point process (object=rectangle) with marks as the length and width of the rectangle. Figure B shows a realization of the point process regarding the information extracted from ...
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2answers
945 views
How to generate nD point process?
Context:
Poisson point processes (PPP) are widely discussed in the literature.
In the following figure a framework to generate two-dimensional PPP is demonstrated. First the area being studied (part ...
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2answers
342 views
How to define marked point processes?
Background:
In mining engineering, sampling is used to get the rate of concentration of minerals in rocks. Sampling procedure is carried out in the field on the area being explored at the predefined ...
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0answers
175 views
Moments of function of Poisson process
Mirror thread on Mathoverflow.
(I'm new to Poisson processes, so please edit if my terminology is incorrect.)
This is a special case of a problem I'm working on; hoping for intuition that will ...
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0answers
96 views
How to denoise a “Poissonous” time series
I have $N$ time series each of which can be modeled as $$y_{kt}=Ax_{kt}+b+\varepsilon_{kt}\quad(1\le k\le N,1\le t\le T),$$ where $x_{kt}\sim\text{Pois}(\lambda\Delta t)$ and $\varepsilon_{kt}\sim ...
5
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1answer
180 views
When doing quadrat counting, how do you construct the quadrats?
I want to perform quadrat count analysis on several point processes (or one marked point process), to then apply some dimensionality reduction techniques.
The marks are not identically distributed, ...
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2answers
473 views
How to find relationships between different types of events (defined by their 2D location)?
I have a dataset of events that happened during the same period of time. Each event has a type (there are few different types, less then ten) and a location, represented as a 2D point.
I would like ...
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2answers
237 views
Correlation of two 1d point processes with non-uniform unconditional distribution
I want to measure the correlation between two 1D point processes $x$ and $y$. Ordinarily I could use the bivariate K-function
$K(t) = \frac{T}{n_xn_y} \sum_{i=1}^{n_x} \sum_{j=1}^{n_y} w(x_i,y_j) ...
5
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1answer
1k views
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 $T^1 = t^1_1, t^1_2, ..., t^1_n$ and $T^2 = t^2_1, t^2_2, ..., t^2_m$ ...
