Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [variogram]

A plot or function used in spatial statistics (or in time series analysis) to describe the degree of spatial (or time) dependence of a stochastic process.

Wikipedia has an article https://en.wikipedia.org/wiki/Variogram with further references.

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Generating data to follow given variogram

It is a straightforward approach having a set of coordinates (e.g., in 2D as {x,y}) and at least an associated variable (e.g., v) to calculate a variogram as a descriptor of the spatial dependency of the variable v through the field being studied. …
Developer
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Issues with ordinary kriging

I was following this wiki article related to ordinary kriging Now my covariance matrix looks like this, for 4 variables 1 0.740818220681718 0.548811636094027 0.406569659740599 0.740818220681718 1 0.740818220681718 …
user34790
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What is the nugget effect?

I don't understand exactly what is meant by the term "nugget effect" in geostatistics. When looking at empirical variograms plotting the variogram $\gamma(h)$ vs. the lag $h$, the nugget is defined as the discontinuity from the origin when the lag…
MachineEpsilon
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Is there an intuitive interpretation of a negative variogram "nugget" value?

A variogram plots the variance of the difference between sample pairs on a field (any dimensionality) against spatial separation (the "lag") of those samples. The extrapolation from observed small-lag variances to a zero-lag variogram value is…
timday
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Creating variogram for a 10,000 set data

I am trying to create a variogram for a data set with 10,000 points. However, if I try to actually calculate the distance of each point with the other then I will have 10,000*9999/2 pairs. Out of these pairs of distances I can round off the distance…
user31820
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Weights in the fit.variogram method of gstat

I'd like to know if I understood correctly the following. In the fit.variogram method of the gstat library, there is a fit.method argument. In the documentation, it says that: The default method uses weights $N_h/h^2$ with $N_h$ the number of…
Robert Smith
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Matrix singularity issues with gaussian variogram

I have defined my gaussian variogram like this $r(h) = \text{nugget} + \text{partial_sill}\cdot(1 - \exp(-\frac{3h^2}{\text{range}^2}))$ I set nugget = 0.1343 partial_sill = 0.3125 range = 19.8642 I tried to create a variogram for a spatial grid of…
user34790
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Creating a variogram for geographical data

I want to create a covariogram for a certain field R distributed on a geographical area. Which sort of packages are available to calculate covariogram. Also the distance metric is geographical distance rather than simple euclidean as in the case of…
user31820
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Fitting a variogram model with the pairwise distance matrix supplied

I'm trying to fit a variogram to my data, however the spatial points are confined by an irregular polygon. So I'd like to supply a variogram model function with the distance matrix of the points. I've looked through gstat, geoR and vardiag but I…
smccain
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What effect does data averaging have on the variogram?

What effect does data averaging have on the variogram? To be specific, please see a simple example: #Simulate a pure random walk data set, call this *PROCESS A* n <- 1000 #number of data points t <- 1:n #time y <- cumsum(rnorm(n)) #data points #…
T_D
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Strange results in kriging with geoR. Is this a bug? Am I doing something silly? Or is this data set just unfortunate?

I am performing kriging on a large number of relatively modest data sets (144 data points on a 9 x 16 grid in each data set). I was experimenting with different variogram models and other parameter tweaks to record errors, and noticed some data…
jonD
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Confusion related to estimation of nugget

I am generating some simulated data from a multivariate gaussian distribution with a covariance matrix sigma. To add some noise, I added an identity matrix to the covariance matrix which depicts gaussian white noise. I then drew some samples from…
user34790
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Issues with fitting a variogram

I am trying to fit a spherical variogram to some synthetic data using the code available at http://www.mathworks.com/matlabcentral/fileexchange/25948-variogramfit. However, I have some doubts. I simulated some synthetic data using GMRF with the…
user34790
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How do you express the variogram $\gamma(u)$ in terms of correlation for a stationary process?

The Analysis of Longitudinal Data textbook by Diggle et al. (2002) mentioned twice (p48 f. and then on p82) that given the following definition of the variogram, \begin{equation} \gamma(u) = \frac{1}{2}\mathrm{E}[\{Y(t) - Y(t-u)\}^2], \quad u \geq…
ning
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Calculating R-squared values from a semivariogram

I have some spatially autocorrelated vegetation data, and would like to know the how well tree size measured at one location can predict tree size in plots 100m away. I've made a semivariogram of the data, but am wondering if I can calculate an R…
jay
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