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Questions tagged [random-field]

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Dirichlet distribution centered at a gaussian random field?

I created three (100x100) synthetic images using values randomly drawn from a Dirichlet distribution as shown below. Each image represent the abundance values of some surface components (soil, water ...
geode's user avatar
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1 vote
0 answers
21 views

Convergence criteria for random field

I am iteratively solving a stochastic equation by generating a random field and using the resulting generation to move toward an equilibrium. I know that the system converges but I want to use an ...
Charles Wetaski's user avatar
1 vote
0 answers
37 views

Probability for all points on a path in a gaussian random field

I have a gaussian random field $u(x)$, $x \in R^2$ , with a covariance function $C(d)$ and I need to calculate probability $P[ u(x) < u_0, \forall x \in S]$, where $S$ is a straight segment in $R^2$...
Anatoly's user avatar
  • 111
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0 answers
64 views

What am I not understanding about semivariogram and Normal Score Transformation?

I have generated this two dimensional random field: This is done following this page. In particular, I have selected t=23 as dataframe and I have changed some parameters. As you can noticed, I have ...
diedro's user avatar
  • 111
1 vote
1 answer
78 views

Generate a syntetic log-normal two dimensional random field

I would like to test some functions that I wrote related to the kriging applied to rain data. In order to do that, I would like to generate a synthetic log-normal 2D random field. The idea is to ...
diedro's user avatar
  • 111
1 vote
0 answers
16 views

"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 $R(h)$ ...
Massimiliano Romana's user avatar
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0 answers
99 views

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's user avatar
11 votes
1 answer
2k views

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. ...
asdf's user avatar
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1 answer
60 views

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 ...
Heathcliffe's user avatar
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0 answers
171 views

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 ...
Joker3139's user avatar
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42 views

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 ...
Shahram Khazaie's user avatar
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1 answer
51 views

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)$....
Optimus's user avatar
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3 votes
0 answers
117 views

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 $\...
jjet's user avatar
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5 votes
0 answers
79 views

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 $T$). ...
Bothorth's user avatar
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