Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

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.

A point process is a stochastic process in which the data are sets of points ordered in a mathematical space. A common example is points which are ordered in time. If the arrival of each point is independent of those that preceded it, and all points have the same arrival rate, the interarrival times will be exponentially distributed. Such a process is called a Poisson process. The distribution of the total number of points occurring within a given temporal interval will be Poisson.

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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) spaced time series - are there (at least) any…
Qbik
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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 $T^1 = t^1_1, t^1_2, ..., t^1_n$ and $T^2 = t^2_1, t^2_2, ..., t^2_m$ and I want to determine if the events in $T^1$…
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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) or are they tending to gather together in some…
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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 to check if there is any correlation between types…
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How to construct quadrats for point processes that differ greatly in frequency?

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, i.e., some marks are appearing quite often, and…
Wookai
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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 good way to measure the correlation between two…
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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 build a point process in the middle with intensity…
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Spatial Point Process: Does an inhomogeneous first order intensity function affect the second order dependence?

As the title suggests, I am having a bit of confusion on the effect of first order intensity function. If I have a first order intensity function that says in a certain region the points are much more likely to occur, that means there would be a lot…
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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 of space which can be in 1D, 2D, 3D, ..., in our…
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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 $\varepsilon_{kt}\sim N(0,\sigma^2)$. Parameters $A$, $b$ and $\sigma^2$…
ziyuang
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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!
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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 point processes. The problem has to do with the…
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Under what circumstances is the log likelihood function of a point process concave?

I am trying to understand under what circumstances the log likelihood function of a point process concave. Assume that the process can be defined by a conditional intensity function and that the log likelihood function exists. Is there a general…
graffe
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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 array of ordered pairs of random x's and random y's…
J Kelly
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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) I[d(x_i,y_j)
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