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72 votes
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40,000 neuroscience papers might be wrong

On the 40000 figure The news are really sensationalist, but the paper is really well founded. Discussions raged for days in my laboratory, all in all a really necessary critique that makes ...
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  • 15.9k
39 votes

Entropy of an image

“What is the most information/physics-theoretical correct way to compute the entropy of an image?“ An excellent and timely question. Contrary to popular belief, it is indeed possible to define an ...
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30 votes
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What is the rationale of the Matérn covariance function?

In addition to @Dahn's nice answer, I thought I would try to say a little bit more about where the Bessel and Gamma functions come from. One starting point for arriving at the covariance function is ...
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25 votes
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What statistical model or algorithm could be used to solve the John Snow Cholera problem?

Not to give a complete or authoritative answer, but just to stimulate ideas, I will report on a quick analysis I made for a lab exercise in a spatial stats course I was teaching ten years ago. The ...
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  • 294k
20 votes

What is the rationale of the Matérn covariance function?

I do not know, but I found this question very interesting and here's what I got after a bit of reading on it. For certain values of $\nu$, the Matérn covariance function can be expressed as a product ...
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  • 518
19 votes

What statistical model or algorithm could be used to solve the John Snow Cholera problem?

In [1,§3.2], David Freedman suggests an essentially negative answer to your question. That is, no (mere) statistical model or algorithm could solve John Snow's problem. Snow's problem was to develop a ...
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17 votes
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How Does Kriging Interpolation work?

This answer consists of an introductory section I wrote recently for a paper describing a (modest) spatio-temporal extension of "Universal Kriging" (UK), which itself is a modest generalization of "...
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  • 294k
15 votes
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Statistical significance of difference between distances

The question of "significantly" different always, always presupposes a statistical model for the data. This answer proposes one of the most general models that is consistent with the minimal ...
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15 votes
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Ordinary kriging example step by step?

Apart from this answer, there are also some nice additional answers to a similar question on gis.stackexchange.com First I'll describe ordinary kriging with three points mathematically. Assume we have ...
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  • 518
13 votes
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What does "irregularly spaced spatial data" mean?

A lot of techniques assume that data is sampled at regularly-spaced intervals. You might count how much litter is near each mile marker on the highway, or sample points in a forest on a regularly ...
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  • 19.5k
11 votes
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Intrinsic spatial stationarity: doesn't it only apply for small lags?

Yes and no. Yes I recall that Andre Journel long ago emphasized the points that Stationarity assumptions are decisions made by the analyst concerning what kind of model to use. They are not inherent ...
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10 votes

How do I combine predictions of four Poisson regressions that use the same independent variable?

Let's Think About Restrictions If you want to the predictions of each quadrant to sum to the total, you have to incorporate that restriction into the model. Presently, there is nothing relating the 4 ...
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9 votes
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Why do you have to provide a variogram model when you are kriging?

Introduction and Summary Tobler's Law of Geography asserts Everything is related to everything else, but near things are more related than distant things. Kriging adopts a model of those ...
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9 votes
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Homogeneous vs. Inhomogeneous Poisson point process

A homogeneous Poisson point process is also called complete spatial randomness described by a single parameter called the intensity (number of points per unit area). It distributes a random number of ...
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9 votes
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What is the interpretation of eps parameter in DBSCAN clustering?

Epsilon is the local radius for expanding clusters. Think of it as a step size - DBSCAN never takes a step larger than this, but by doing multiple steps DBSCAN clusters can become much larger than eps....
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9 votes
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How, in practice, are spatial covariances determined?

To expand on my comment, commonly "spatial covariance" is associated with Gaussian Processes, which are typically assumed to be stationary. Furthermore, in practice the spatial covariance function (...
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  • 12.2k
8 votes

Entropy of an image

There is none, it all depends on the context and your prior information. Entropy has many interpretations such as "measurement of order" or "measurement of information", but instead of looking at the ...
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  • 147
8 votes

Why does the first eigenvector in PCA resemble the derivative of an underlying trend?

Let's ignore the mean-centering for a moment. One way to understand the data is to view each time series as being approximately a fixed multiple of an overall "trend," which itself is a time series $...
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  • 294k
8 votes
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Is Maximum Likelihood implemented differently in different supervised classification systems?

You should not expect the same results using different software. "Maximum likelihood" is a general term for a common way of estimating parameters for a statistical model: attempt to find the values of ...
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8 votes
Accepted

What is the expected distance to the nearest molecule?

Consider $d$ dimensions. The distribution to the nearest neighbor of any point can be approximated by supposing $N$ neighbors are independently, uniformly, and randomly situated within a radius of ...
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  • 294k
7 votes
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What is the difference between (universal) kriging and spatial autoregressive models?

Short answers: 1) As you said the difference between the two is only in the spatial structure. 2) A lot of people work to find an equivalent mathematical formulation between the two, especially in ...
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  • 1,180
7 votes
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Any easy way to cluster GPS trajectories?

There is no easy way. there is no universally useful accepted definition of what is a cluster, so how could you do clustering? Similarity is not objective. If you use e.g. DTW then you do assume the ...
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7 votes

What is the proper way of calculating the kernel density estimate from geographical coordinates?

You might consider using a kernel especially suitable for the sphere, such as a von Mises-Fisher density $$f(\mathbf{x};\kappa,\mu) \propto \exp(\kappa \mu^\prime \mathbf{x})$$ where $\mu$ and $\...
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  • 294k
7 votes

Data partitioning for spatial data

Nice question, and I fully agree with Roozbeh. Spatial cross validation is relevant when you have spatial autocorrelation in your training data that usually occur when your data are clustered in ...
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  • 71
7 votes

Data partitioning for spatial data

After watching the video, I have become more confident that this application is more like "data reproduction", where a random partitioning is OK, rather than "data prediction". To me, you justify ...
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  • 481
6 votes
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Use of Poisson distribution to analyse distribution of individuals in space

Your understanding is basically correct, and this kind of analysis is much older than your reference Choosing and Using Statistics: A Biologist's Guide Paperback Such a model is called a Poisson ...
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6 votes
Accepted

Why is Moran's $I$ coming out greater than $1$?

Comparison of $I$ with correlation coefficients is good, but it has its limits. This answer uncovers what those limits are. It derives a tight upper bound for $|I|$ in terms of the weights matrix $W$...
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  • 294k
6 votes

What does "irregularly spaced spatial data" mean?

Good answers by Matt (+1) and others. Just to have a picture to drive the message (visually) home. In the following figure assuming that the squares represent sampling points the grey boxes follow an ...
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  • 36.2k
6 votes

What is the interpretation of eps parameter in DBSCAN clustering?

The meaning of $\epsilon$ is that of the neighbourhood size. The neighbourhood of a point $p$, denoted by $N_{\epsilon}(p)$, is defined as the $N_{\epsilon}(p) = \{q \in D | dist(p,q) \leq \epsilon \}$...
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  • 36.2k
6 votes
Accepted

beta-regression accounting for residual spatial auto-correlation in R

We can think of our observations as arising from some distribution with a mean structure component and a covariance component. Essentially we have $$y = \boldsymbol{X\beta} + \mathbf{Zb} + \epsilon$$ ...
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