Questions tagged [covariance-function]
7 questions
4
votes
0 answers
Deriving spectral measure
While reading this book, I got stuck on page 266 where the authors found the spectral measure $F(du)$ of the generalized covariance function $K(h) = \Gamma(-\alpha/2) |h|^{\alpha}, ~0<\alpha<2.$ $F(du)$ and $K(h)$ are related through the identity…
Shanks
- 743
- 1
- 5
- 18
3
votes
0 answers
Gaussian process regression - Count data inputs
I have a research problem where I want to build an emulator (surrogate/metamodel) for a stochastic computer model for efficient uncertainty & sensitivity analysis. The go-to here is to run the computer model a handful of times and then perform a GP…
jcken
- 2,092
- 5
- 17
2
votes
2 answers
What is meant by this idea that a covariance function of a Gaussian process "induces" properties? And what is the connection to stationarity?
I am currently studying the textbook Gaussian Processes for Machine Learning by Carl Edward Rasmussen and Christopher K. I. Williams. Chapter 1 Introduction says the following:
The specification of the prior is important, because it fixes the…
The Pointer
- 1,064
- 13
- 35
1
vote
1 answer
Isotropic covariance functions on a lattice in $R^n$
In many spatial statistics references, isotropic covariance functions are usually defined in terms of Euclidean distance. But does this generalize to different norms on $R^n$? For example, if we took the exponential covariance…
HelloKitty
- 13
- 2
0
votes
0 answers
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
- 33
- 6
0
votes
1 answer
Different regression models in clusters, same variance structure
I have data that can be clustered so that each cluster has its own set of both observations and variables. I want to fit a linear model on each cluster, but i want the clusters to share the same variance structure (and thus estimate parameters of…
Janusz
- 3
- 1
0
votes
0 answers
Confirming the formula for the Spectral Density of a Matern Covariance Function
The Matérn Class of functions is given by $$k_M(r)=\frac{2^{1-\nu}}{\Gamma(\nu)}\left(\frac{r\sqrt{2\nu}}{l}\right)^{\nu} K_{\nu}\left(\frac{r\sqrt{2\nu}}{l}\right)$$ where $r=\Vert x-x'\Vert$. The function $K_\nu$ is the Modified Bessel of the 2nd…
An old man in the sea.
- 5,070
- 3
- 23
- 57