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0answers
9 views

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 ...
0
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0answers
9 views

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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0answers
6 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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1answer
11 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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0answers
7 views

Generating random point process in Excel [on hold]

I need to generate random point process manually to learn in the same way they do in other software like arc esri. I can use RAND() but I know what I produce then ...
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0answers
7 views

Is Moran 1 Point process analysis? [on hold]

I use arc software to do Moran 1 analysis and it only takes polygons for input. Why is it called point process of only takes polygons?
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2answers
18 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
36 views

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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1answer
18 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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0answers
8 views

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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0answers
11 views

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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0answers
10 views

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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0answers
8 views

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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0answers
7 views

Standard deviation of point pattern [migrated]

I am using ArcGIS software to create a Standard deviation of point pattern, and I know whether Ii need to expect a circle or an ellipse. Is standard deviation in that context always circular? And if ...
0
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1answer
22 views

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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0answers
11 views

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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0answers
12 views

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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0answers
13 views

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 ...
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0answers
56 views

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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0answers
7 views

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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1answer
54 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 $A$, ...
3
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0answers
25 views

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. ...
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0answers
32 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 ...
2
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1answer
73 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 ...
3
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1answer
113 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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0answers
15 views

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 ...
0
votes
1answer
97 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 ...
2
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0answers
32 views

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. ...
3
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1answer
97 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 ...
2
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1answer
433 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 ...
1
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0answers
73 views

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 ...
0
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0answers
47 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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0answers
32 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 ...
2
votes
1answer
202 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 ...
1
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0answers
27 views

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 ...
3
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2answers
271 views

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 ...
4
votes
1answer
142 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 ...
1
vote
1answer
64 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 ...
5
votes
1answer
439 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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0answers
111 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 ...
4
votes
2answers
118 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!
2
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0answers
164 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
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1answer
118 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, ...
3
votes
1answer
441 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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3answers
184 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
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0answers
107 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
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4answers
1k 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
742 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?
6
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2answers
178 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 ...
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3answers
2k 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) ...