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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46
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6answers
16k 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) ...
9
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1answer
851 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 ...
15
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1answer
6k 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 $T^2 = t^2_1, t^2_2, ..., t^2_m$ ...
1
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0answers
261 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 ...
6
votes
2answers
247 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 ...
10
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3answers
5k 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) ...
5
votes
0answers
652 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 ...
2
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0answers
149 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 non-...
2
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1answer
2k 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?
3
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2answers
3k 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 ...
9
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2answers
707 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 ...
4
votes
1answer
239 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 ...
4
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1answer
1k 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 ...
3
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2answers
205 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 ...
1
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0answers
47 views

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 ...
1
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1answer
31 views

Do quadrats have to be equal in size?

I'm doing a quadrat analysis of point pattern. My study area is 2.3m by 2.3m. Can I have quadrats of 1sqm or does it have to be equal area? If quadrats are 1sqm, then four of them would be of full ...