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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857 views

Difference between time series prediction vs point process prediction

I am working on a problem of predicting event counts based on user history. This is a classical time series analysis problem, and I used the ARIMA model: (wiki). I also applied a Hawkes point process ...
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Good resource for p-thinning of a point process

Can you please tell me what is a good resource about p-thinning of a point process and then finding the distance between the original and obtained process? Something like the Kullback Leibler distance,...
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point patterns and line segment patterns

How could I attach points to the line segment pattern using R language Function for example I have point pattern on linear network and I have marked line segment pattern I try to attach points in ...
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74 views

Minimum interval such that $X\%$ of intervals will contain $\ge Y$ events

I have a data set that contains the dates and times of purchases. Say I have one month of data for the purchases. I am looking for the interval of time, say 10 mins / 30 mins / hourly, for which 90% ...
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1k views

How to compute the firing rate of a neuron with different duration of trials?

I have recorded data from a neuron from different trials. Each trial we show a stimulus to a rat and then we measure the neural activity. I want to measure the PSTH which is peristimulus time ...
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Find the most frequent timespan of event occurrence

I'm working on bike-robbery events dataset. I'm trying to figure out the most frequent timespan of a bike robbery. Most of time, the robbery does not occur when the owner is watching => the declared ...
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124 views

Does anyone have real world example for random point pattern

I have been writing a paper and need to give examples for the different patterns that are result of point process. It has to be real world examples. For clustered I give the example of settlements and ...
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67 views

Can random point process generator generate pattern that is not random?

I am using esri arc to generate random points. I then analyze the pattern from this process using Average Nearest Neighbor which is also in esri gis but lets say it can be in any other software. Is ...
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95 views

Point Pattern Analysis- what is it good for

OK so I now know my point data is Random. Brilliant. But now what? How does it add anything to the understanding of the data? Sorry if that's a basic question but I honestly don't know what Point ...
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4answers
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What is the best test to check if pattern is uniformed?

Out of the following, which tests are best to use on uniformed data to make sure it is indeed dispersed $\chi^2$ Simple NNA High/Low clustering (Getis - ord) KNN (Ripley) Moran Monte Carlo
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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 ...
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Effectiveness of mean centre and intensity

I am describing the Cells dataset (B.D. Ripley Modelling Spatial Patterns 1977) using numeric values of: intensity mean center Possibly standard deviation I cannot add maps but just present the ...
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Who came up with the term “complete spatial randomness?”

I've seen the term "complete spatial randomness" widely used in literature but can't figure out who was the first to coin it. Who originated it, and is there a paper it can be cited to?
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PPA- what are Regular, Random, Normal and Clustered?

In Point Pattern Analysis a particular dataset can be one of four, at least according to Wikipedia: Clustered, Normal, Random or Regular. The four: What is the name of those four options? Point ...
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191 views

Expected Value in Poisson Point Process with Prior Knowledge

I have a setup with a homogeneous Poisson Point Process (PPP) of intensity $\lambda$ in $W \subseteq \mathbb{R}^d$ and a set $A \subseteq W$. I'm looking for the expected value of points in set $A$, ...
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Critical scale of variation of tree biomass using variography

I have a combination of a philosophical and a technical question. I am interested in an application where I am trying to find a critical scale of autocorrelation of tree biomass on the landscape. Let’...
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231 views

Spatial point process: Homogeneous vs inhomogeneous K-function

I wonder when would you use a homogeneous K-function instead of a inhomogeneous one and what advantage it has over inhomogeneous K-function? In my opinion I think we should always use inhomogeneous ...
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306 views

Regression-like models for spatial point processes restricted to a network or grid

I am working on a spatial analysis of traffic accidents, the goal of which is to estimate the effects of spatial covariates on the intensity function of crashes. The original analysis was an ...
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300 views

Inter-arrival time of subsampled Poisson point process

Suppose that I draw $n$ points from a Poisson point process of rate $\lambda$, i.e. with inter-arrival times distributed i.i.d $\sim \text{Exp}(\lambda)$. Now suppose that I choose $m < n$ of ...
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781 views

Bivariate K function for inhomogeneous spatial point processes

I have some inhomogeneous spatial point patterns of individuals in a cactus population. I also have marks, such as "diseased"x "healthy" individuals, and "adult" x "juvenile". I've already computed ...
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Polygon pattern analysis -> point pattern analysis?

Is it correct to convert polygons to points in order to do a point pattern analysis ? I have a set of polygons that tend to be clustered around roads in a study area. I just want to show this fact. ...
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288 views

Use of Poisson distribution to analyse distribution of individuals in space

Dytham 2010 suggests using the Poisson distribution to establish whether individuals are evenly distributed in space. Say we end up with a map of individuals in a study site that looks like the ...
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3k views

Homogeneous vs. Inhomogeneous Poisson point process

What are the main theorical differences between the homogeneous and inhomogeneous Poisson point process? What are the aspects and condition of my data that I can determine which point process best ...
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141 views

Quantifying how uniformly spread out points are?

I'm looking for a way to quantify how "clumped" vs homogeneously/uniformly distributed points are in a graph. Each collection has 100 points as (x,y) pairs. I've attached two graphs as an example. ...
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66 views

Simulation of a process consist of Brownian motion and Poisson process

I am trying to simulate the following process: h(t)=B(t)+e[P1(t)-P2(t)] in which B(t) is a Brownian motion and P1, P2 are Poisson process with ...
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114 views

A union bound on a continuous variable

Assume a continuous point process (say Poisson) in [0,t]. Assume that it is given that only three jumps occurred in [0,t], however, their exact time coordinate is unknown. In addition, it is known ...
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748 views

Residuals plot from ripley K function on spatstat

I am a rookie on R and on spatstat package. I would like some help with the Kres function on spatstat. As is always wise to plot the residuals from any kind of ...
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Likelihood Lévy process

Consider af complete observation sample path of a Levy process $X_t$ (wtr a poisson randommeasure $\mu$) on [0,t] concentrated on the integers. The parametrization is a family of Levy measures $\nu_{\...
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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 ...
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476 views

Test hypothesis point process is Poisson [duplicate]

I have some data and I would like to test the hypothesis that they come from a homogeneous Poisson process. I can of course look at the inter event times and test if these are exponentially ...
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106 views

A modelling question about point processes with heavy tails

I am trying to model a number of point processes for which I have data. If I choose to model each one using a (different) homogeneous Poisson process and estimate the rate using MLE then for some of ...
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968 views

What is the difference between (universal) kriging and spatial autoregressive models?

As part of a course on missing observations in social/survey statistics I am trying to explore existing methods of predicting either point pattern or polygon data. I got quite confused by all the ...
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208 views

How to simulate a etas spatio-temporal model?

My question is how simulate the spatio-temporal ETAS point process (a point process used for earthquake prediction) defined by a conditional intensity function. More precisely: let $\mathbf{V}$ be a ...
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194 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!
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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 $g(r)$, ...
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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, ...
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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 ...
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902 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 ...
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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-...
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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 $p=P(v_1<c)=P(v_2<c)$, ...
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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?
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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 ...
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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) ...
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779 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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668 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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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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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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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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240 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 ...
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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 ...