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2
votes
2answers
47 views

Similarity measures for point processes

I have multiple measurements of a point process: vectors of 0's and 1's. I'm trying to gauge the similarity of the measurements, but have no idea how to proceed. Any suggestions? Thanks!
0
votes
0answers
7 views

How can I compare the deviation from CSR in different point patterns?

I recently discovered the many tools of point patterns analysis and this is a very interesting field. I read a lot about how to look for deviations from complete spatial randomness (CSR) and I am ...
0
votes
0answers
14 views

Metric to show the overall similarity between two set of points obtained from handwritten word?

In my case, I would like to compare different handwriting to a template handwritten word, and return a single metric to show how closely the input matches the template's shape. The lines are the same ...
2
votes
0answers
19 views

Maximam r distance for Ripley's K-function

I am using R's package spatstat to study the locational pattern of conflict events in Africa (around 8.000 points) using point pattern analysis techniques. I was able to obtain the plot of g(r), the ...
3
votes
1answer
74 views

Predicting a continuous outcome using point process descriptors

I have measured a series of times for discrete events along with a continuous variable. So essentially I measure a point process $P: t_1, t_2, \dots, t_n$ and values $A_1(t=x_1), A_2(t=x_2), \dots, ...
2
votes
1answer
96 views

What's so Poisson about a Poisson Point Process? (or, can I generate one using random ordered pairs?)

I know there is an R spatstat function to generate a ppp (Poisson Point Process), but I'm working in python, and I am not clear what spatstat.ppp is doing behind the scenes. If I generate a an ...
0
votes
0answers
26 views

How to model ties between two event sequences?

Context I have two processes that each emit an event at various times: ...
3
votes
2answers
87 views

Measuring correlation of point processes

There is a huge literature on time series analysis. My data does not seem to fit into the standard model in that it consists of event times, that is the times at which an event occurs. What is a ...
2
votes
0answers
76 views

Conditions for Poisson approximation of the superposition of non-Poisson processes

It is well known that the superposition of $N$ Poisson processes is itself a Poisson process with an intensity given by $\sum_{n=1}^{N} \lambda _{n}$. Conversely a superposition including any ...
5
votes
4answers
544 views

Superposition of two dependent Poisson processes

$N_1(t)$ and $N_2(t)$ are two independent Poisson processes with intensities $λ_1$ and $λ_2$ respectively. $v_1$ and $v_2$ are two dependent positive random variables, and $p=P(v_1<c)=P(v_2<c)$, ...
1
vote
1answer
217 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
votes
1answer
123 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 ...
9
votes
3answers
1k 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
votes
1answer
119 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 ...
5
votes
0answers
193 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) = ...
21
votes
6answers
1k 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) ...
1
vote
0answers
50 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 ...
1
vote
0answers
69 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 ...
2
votes
0answers
112 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 ...
3
votes
2answers
130 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 ...
4
votes
2answers
472 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 ...
4
votes
1answer
169 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 ...
4
votes
0answers
243 views

Dependent thinning Poisson process

If $N_1$ and $N_2$ are independent Poisson processes then the superposition is a Poisson process. Is it possible to construct two dependent Poisson processes such that the superposition is a Poisson ...
3
votes
1answer
92 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 ...
0
votes
0answers
135 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 ...
7
votes
1answer
300 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 ...
2
votes
1answer
1k 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 ...
1
vote
0answers
143 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 ...
5
votes
2answers
2k 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 ...
2
votes
2answers
479 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 ...
0
votes
0answers
234 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 ...
4
votes
0answers
121 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 ...
8
votes
1answer
234 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, ...
9
votes
2answers
541 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 ...
3
votes
2answers
303 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) ...
7
votes
1answer
2k 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 $T^2 = t^2_1, t^2_2, ..., t^2_m$ ...