Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [random-field]

12 questions
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Questions regarding geodesics in Adler and Taylor's "Random Fields and Geometry"

I'm working through some calculations in Adler & Taylor's Random Fields and Geometry. $f$ is a real, scalar, zero-mean random field parametrized by $x^i$ (elements of some topological space $T$). Using commas to denote partial derivatives $f_{,i}…
Bothorth
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Relation between Gaussian Processes and Gaussian Markov Random Fields

As a non expert in the field, I am relating Gaussian Processes (GP) and Gaussian Markov Random Fields (GMRF). I might just be confused by the fact that different resources use different formalism. Here I try to report the main definitions and my…
asdf
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What conditions are needed for a differentiable random field?

I've been playing around with some random field models and noticed that the apparent differentiability seems to be related to the covariance function's behavior at 0. My initial guess was that if $\frac d {dx} C(x) = 0$, then a resulting random…
jjet
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"Nonlinear" random spatial field: an example

I want to generate a "nonlinear" random spatial field in the sense that the autocorrelation function in function of the lag/distance $h$, $\rho(h)$, should be not equal to the $R(h)$ coefficient that is $R(h) = \sqrt{1-exp(-2I(h))}$, where $I(h)$ is…
Massimiliano Romana
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Does bi-spectral function completely describe the non-Gaussian feature of a random field?

Suppose we have a density field $\delta$, and denote the Fourier transform of which by $\hat{\delta}$. We denote the Dirac delta function by $\delta_D$. The power spectral function is defined by the equation…
user332352
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How to interpret level set threshold for the posterior spatial random effect from a Log-Gaussian Cox process?

For a Log-Gaussian Cox process, the prior distribution is a zero-mean Gaussian process. But for the posterior distribution, it is analytically intractable and it is not a Gaussian process anymore. So then my question is how do we interpret a…
NamelessGods
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Gaussian random fields and multiple-output Gaussian processes

This CV post asks about the definition of a multiple-output Gaussian process. Although the definition seems to be clear that a multiple-output Gaussian process is a ''Gaussian process'' that gives us a vector response…
Henry.L
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What is the spatial covariance algorithm?

Given a realization of a spatial random field, what is the algorithm to determine the spatial covariance, or the covariance function of the spatial lag? Many thanks.
Massimiliano Romana
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Probability of path between two points in excursion set of (Gaussian) random field

The Adler paper "On the existence of paths between points in high level excursion sets of Gaussian random fields" discusses the asymptotic limit of path probabilities in Gaussian random field excursion sets. But they make the assumption that a path…
Heathcliffe
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Repeated measures test against baseline

I have data from a field experiment and I want to identify if it's reasonable to test against a baseline mean to show that the ratings are significantly greater. These are the characteristcs of the intervention delivery and the measurements: Ten…
Joker3139
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Spatial auto-correlation function of $\sin^2(2\theta)$ in terms of that of $\theta$

Let $\theta$ be an isotropic random field which has a unifrom pdf $U[0,2\pi]$ and whose auto-correlation function is $R_{\theta \theta}(|y-x|) = \mathbb{E}[\theta(x)\theta(y)]$ wherein x and y are space variables. Is there a way to relate the…
Shahram Khazaie
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Finding probability of at least one RV taking a specific value

Given a set of random variables $X = \{X_1, X_2, .. X_N\}$ where the domain of $X_i$ is $ \{ l_1, l_2, .. l_K \}, \forall i \in \{1,2 ... N\}$. I want to compute $P($ for at least one i, $ X_i = l_k)$. What is the best way to compute it?
Optimus
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