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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.

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How do nugget interactions work in Gaussian Processes/Kriging?

How do nuggets and nugget interactions fit into the variogram framework? I am especially interested in the case where there is more than one distance term being used (e.g. space and time): where you ...
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131 views

Problems fitting a model to a variogram

I am having problems fitting a variogram model. I tried to change some parameters to estimate or fix them but I am still not achieving any improvement. I remove trend of the data and use logarithms ...
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Rational selection of “weighted” (logic tree-based) combination of two or more exponential variograms

I've been asked to combine two or more theoretical variograms with exponential functional forms, using a "logic tree" approach to assign a subjective weight to each constituent variogram representing ...
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26 views

Cokriging, zero distance semivariance [gstat]

Trying cokriging with simulated data, I faced a problem that did not seem one in the demo(cokriging) with the meuse dataset: I can't use ...
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42 views

How to interpret semivariogram parameters from two different raster images?

I know the definitions of the components of a semivariogram. However, I would want to know how they could be interpreted when applied to actual scenarios. For instance, I have two EVI (enhanced ...
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62 views

How can I understand these variograms?

Using grf function from R package geoR, I simulated 6 replicates (each with 1000 samples) of a Gaussian random field on ...
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71 views

Mixed model with serial correlation and random slope?

I'm making a mixed model for some longitudinal data, where the response is measured fro multiple individuals over time. I have made a model with random intercept, random slope and gaussian serial ...
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2answers
3k views

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 ...
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262 views

Temporal Variogram

Can we compute temporal variograms just like spatial variograms? I know about spatio-temporal variograms but I am more interested in doing a comparison of separate spatial and temporal variograms and ...
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1answer
98 views

How do you interpret this variogram?

Description: 8000 spatial data points spanned over an entire state 200 bins are used My question: Is the variogram telling something about the nature of the data? Why is it fluctuating? Should I do ...
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329 views

Spherical vs. Exponential Kriging Covariance Functions

A statistical epidemiologist colleague of mine told me that in comparing spherical vs exponential kriging covariance functions, only the latter (i.e., exponential) function is generally a valid model. ...
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1answer
148 views

How SHOULD a variogram plot look like?

Say you fit a model m. You then calculate the variogram. In R, this can e.g. be done by using plot.Variogram using the nlme package on an lme object. Say the plot indicates that yes, there is some ...
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63 views

Explain Like I'm Five version for Variograms in R's gstat package

Long story short, I asked a question on StackOverflow about Variograms in the gstat package in R. The person who answered gave me some tips on creating the variogram using the package. My dataset is ...
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244 views

warning when fitting variogram - gstat

I'm trying to build a variogram model of the semi variance in Zn concentration with distance using gstat package in R. First I plot the variogram based on my data (it clearly seems to mean that the ...
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28 views

Variogram to constrain kernel density bandwidth

I have linear structures transformed into points and spatially distributed like this: I want to perform a kernel density so that zones with lots of structures present high density. The problem is ...
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222 views

How much difference in the Akaike Information Criterion is reasonable between a Spatial and a Non spatial Model

I am doing supervised land value modelling (900 observations) and I am comparing two approaches to do a variable selection (51 variables). I am using R. The first one is a backward step-wise ...
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1answer
298 views

Why is positive definiteness necessary for kriging?

I understand from wikipedia that a variogram model must be positive definite to be used for kriging: Note that the experimental variogram is an empirical ...
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30 views

Is there a way to find optimal sensor node locations in a domain when all data is known?

I have an x-y domain where I know the snow depth everywhere. (i.e. the granularity of the values is such that I can assume I know it everywhere). I want to use this information to inform where to ...
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25 views

I am not sure if my data are spatially autocorrelated or not.

I have been trying to figure out if my data are spatially autocorrelated by generating semivariogram of the residuals. I do not get the shape similar to any variogram (spherical, exponential or ...
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108 views

What is the computational complexity of the empirical variogram?

If we use the method of moments estimator: $2\hat{\gamma}(h) = \frac{1}{| N(h) |} \sum_{N(h)} (Z(s_i) - Z(s_j))^2$ What is the computational complexity? My initial assumption was that it would be $...
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68 views

Is there an approach to combining variograms?

If we compute two seperate variograms for the same type of measurement, but the areas which they cover overlap, is there a logical way (or does it even make sense) to combine the two variograms? ...
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112 views

Why is my semivariance so high?

I am using variograms checking for spatial autocorrelation in a resiudal pattern produced by a GLMM-NB. In theory, the semivariance should be bounded between 0 and 1 (that´s what I think at least as I ...
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1answer
133 views

What does it mean that a variogram keeps increasing with distance?

I am modeling my 3D dataset with a Gaussian Process with square-exponential covariance. To test whether this is a good model, I subtract the mean from the observed data and then calculate the ...
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1answer
208 views

Kriging: fit.method and dX argument in variogram

I would like to krige residuals (from multiple linear regression) of yearly precipitation totals from a 50 years time series. Every year has been regressed individually. The residuals will be added to ...
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1answer
814 views

Interpreting Spatio-Temporal Variograms

I've got spatio-temporal disease data at the county/annual level for 2000-2014. I'm analyzing it to try to pull out temporal variations in disease incidence and was told that I should generate a ...
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153 views

Variogram with custom distance matrix

I work in marine ecology and as such all of my distance matrices are constructed using the shortest possible marine route - i.e. avoiding any land. Here is a plot of my "marine distances" against "as ...
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Critical scale of variation of tree biomass using variography

I have a combination of a philosophical and a technical question. I am interested in an application where I am trying to find a critical scale of autocorrelation of tree biomass on the landscape. Let’...
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1answer
418 views

Gstat: Modelled semivariogram values not matching plotted model using the variogramLine function

I am trying to extract the semivariance values associated with a given semivariogram model developed in gstat, the end goal being to compare modelled semivariance with observed semivariance at defined ...
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1answer
89 views

Gaussian Mixture Model: bandwidth parameter versus variogram fitting?

I'm estimating a stationary, spatially random variable over a 2-dimensional domain. I have ground-truth measurements in several locations, over time. I need some way of spatially-interpolating ...
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1answer
533 views

Simple Kriging with linear semivariogram

While studying how to develop a simple kriging model with a linear semivariogram, the various tutorials point towards creating a covariogram using $\sigma(h) = \sigma(0) - \gamma(h)$, but the value of ...
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96 views

Non-parametric variogram estimators

I'm working with overdispersed, count spatial data. The goal is to look specifically at spatial dependence patterns. I'm trying to fit variogram models to empirical variograms, however the only ...
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1answer
292 views

Lag lengths are larger than my domain in gstat in R? variogram object

My problem is that the my resulting variograms are of a larger lag length than my domain. I have the following code to compute lags in the vertical direction: ...
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1answer
666 views

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'...
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54 views

Measurament error from semivariogram

I am looking at a model to determine the measurement error for a set of measurements of a spatially correlated phenomenon (sea surface temperature measurements) using a semivariogram technique. For ...
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1answer
255 views

Kriging results are too localized, how can I increase the influence of each data point

I have a small dataset that looks like this... ...
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151 views

AIC or similar selection techniques for Variograms?

I have a very basic question: how does one choose the "best" variogram? It is possible to fit different models to an empirical variogram, e.g. nugget, ...
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1answer
732 views

R Error in chol.default(A) krigeST from gstat package

I am working with an hourly dataset of air temperature, recorded at ~200 stations over a relatively small area. I chose a space-time variogram (e.g. sum-metric) to fit my data and am now trying to ...
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1answer
215 views

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...
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2answers
286 views

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: ...
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110 views

Variance and Variograms: Sigma?

Can someone please walk me through this morass of σ's? There is a sigmasq in the summary output from geoR's likfit. Really this is the one I'd like to know about. I'm not clear which of all of the ...
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114 views

Details on kriging and variograms

I was wondering what are the steps to perform factoring kriging. I know it is used to extract specific components that may have a physical meaning and this is achieved by kriging. However, I have some ...
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276 views

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 ...
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133 views

How do you constrain variogram estimates to be a percentage?

I am interpolating soil texture data with GeoR and ARCGIS. The ordinary kriging process is straight forward and GeoR facilitates cross validation. Has anyone else produced variogram parameters, nugget ...
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238 views

Deriving the ordinary kriging equations with noisy data

I am trying to derive the ordinary kriging equations when I want to estimate the underlying value at $T(x_0)$ from the noisy observations at its neighbors $Z(x_1),....Z(x_n)$. $Z(x_0) = T(x_0) + \...
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1answer
447 views

Issues with ordinary kriging

I was following this wiki article related to ordinary kriging Now my covariance matrix looks like this, for 4 variables ...
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1answer
145 views

Matrix singularity issues with gaussian variogram [closed]

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 ...
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90 views

Confusion related to ordinary kriging

I was reading this wiki article related to ordinary kriging where they calculated the weights like this I know that covariance from the covariogram and semivariance from the semivariogram are ...
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1answer
101 views

How to recover the underlying observations from the noisy ones using gaussian processes

I have some simulated experiments where I generate some samples with an exponential correlation function. I am assuming a spatial grid whose variables form a multivariate gaussian distribution with an ...
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149 views

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 ...
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277 views

Estimating the autocorrelation function with some noisy observations

I am wondering how to estimate the actual correlation function when I have some noisy samples of some space. Lets say, I have a space and the locations in the space are variables following a ...