72
votes
Accepted
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 ...
- 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 ...
- 519
30
votes
Accepted
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 ...
- 2,706
25
votes
Accepted
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 ...
- 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 ...
- 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 ...
- 2,137
17
votes
Accepted
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 "...
- 294k
15
votes
Accepted
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 ...
- 294k
15
votes
Accepted
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 ...
- 518
13
votes
Accepted
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 ...
- 19.5k
11
votes
Accepted
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 ...
- 294k
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 ...
- 27.1k
9
votes
Accepted
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 ...
- 294k
9
votes
Accepted
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 ...
- 1,118
9
votes
Accepted
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....
- 40.1k
9
votes
Accepted
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 (...
- 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 ...
- 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 $...
- 294k
8
votes
Accepted
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 ...
- 1,094
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 ...
- 294k
7
votes
Accepted
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 ...
- 1,180
7
votes
Accepted
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 ...
- 40.1k
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 $\...
- 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 ...
- 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 ...
- 481
6
votes
Accepted
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 ...
- 66.4k
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 $W$...
- 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 ...
- 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 $N_{\epsilon}(p) = \{q \in D | dist(p,q) \leq \epsilon \}$...
- 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
$$y = \boldsymbol{X\beta} + \mathbf{Zb} + \epsilon$$
...
- 39.5k
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