# Tagged Questions

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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### 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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### 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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### How to inferring the casual relation between two point processes? Edit

I have two point processes. One is the spike time of a neuron and the other is when a rat licks the sugar water. I want to find out if there is any correlation and causation between these two ...
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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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### When do I add elevation and time dimensions to my point process analysis [duplicate]

I have points I want to analyze their patterns. The points are of a real world data, let's say crime or settlements in the suburban or anything. I can apply elevation to it and I there is a time for ...
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### Difference between 2D and 3D point process

I have points that have elevation attached to them (they were 2D but then someone from the department of geography helped us applying elevation so now they are 3D). I'm about to explore options for ...
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### 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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### 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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### 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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### 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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### 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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### What is the relationship between Intensity and Quadrats?

In point pattern analysis, what is the relationship between Intensity $\lambda$ and the quadrats analysis? Can $\lambda$ be calculated without or prior to dividing the area to quadrants?
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### Types of nearest neighbor analysis

I hear that there are different nearest neighbor analysis methods. Just nearest neighbor: $d = \epsilon (d)i / n$ But also higher order NNA, K and L NNA, refined NNA etc. Apologies as I don't have ...
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### Standard deviation in PPA

In Point Pattern Analysis I created a Standard deviation with a single degree (not sure what is the unit but $1\alpha$). Is there any use for counting the points within the area created? what does it ...
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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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### Area for nearest neighbor analysis

I'm using a software called ArcGIS to calculate the Nearest Neighbor Z value of the Cells dataset (Diggle 1983): The coordinates I have range as a percentage between 0 and 1. ArcGIS has a wizard ...
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### Characterization of point process, given the number of points

For a point process with independent and identically distributed inter-renewals, with distribution $p(x)$, we observed $N$ points on $[0,T]$. What is the probability distribution function of the event ...
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### Is there such thing called a Uniform point process? (not Poisson point process)

We know a Poisson spatial point process is characterized by the following properties: The Total number of points N follows a Poisson distribution Given N, the point process is a uniform distribution ...
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### Pairwise interaction point processes for forecasting

Does anybody use pairwise interaction point processes for a computational forecasting assuming that we do only observe a finite part of entire supporting set, e.g. we have a pairwise interaction point ...
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### 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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### 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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### 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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### 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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### Point process models

Two of the popular models for analyzing point process data are Cox and Hawkes processes. My question is how do we compare the statistical properties of these two processes as they both can be ...
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### 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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### 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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### 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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### Understanding Poisson Point Process [closed]

Could someone explain the Poisson Point Process? Is it simply an Integration over a Poisson Process for higher dimensions? If so, how do you derive the function, say in two-dimensional space, and 3-...
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### 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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### 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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### 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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### 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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### 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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### 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 $p=P(v_1<c)=P(v_2<c)$, ...