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Questions tagged [kriging]

Kriging is spatial prediction based on a stochastic model of a spatial random field. Such models and methods can also be used in non-spatial context, and then often known as gaussian processes.

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How to handle multiple points at the same location in spatial interpolation?

I am new to the topic of spatial interpolation and would appreciate your opinion on a general question which has arisen. Suppose I have a data set containing rental rates for different apartments in ...
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Poor performance from `gstat::krige` with a noise predictor

I'm new to kriging, and I'm considering replacing a use of inverse-distance weighting (IDW) in a spatial modeling project (implemented with gstat::idw in R) with a ...
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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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Gaussian process with interval observations

The stochastic process $(X_t)_{t \in T}$ is a Gaussian process if the marginal distribution of $X_{t_1}, \ldots, X_{t_n}$ is a multivariate Gaussian distribution for all $t_1, \ldots, t_n \in T$. Let ...
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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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98 views

Correct way to compute the error variance of ordinary kriging

I'm learning ordinary kriging and I found some discrepancies in the method of computing error variance among different materials I read, in general there are 2 different formula: Method 1: ...
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89 views

spacetime R: How to handle missing data in a space-time-full data structure for spatio-temporal kriging purposes?

I am using R and the spacetime package. I am having problems using STFDF. I want to use the STF data-structure since I have spacetime data with recurrent observations for fixed spatial coordinates. ...
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Noisy conditional simulation

A conditional random field $Z_C(x)$ is a random field whose realisations $z_C(x)$ always take the same values $z_C(x_a)$ at locations $x_a$. Realisations of $Z_C(x)$ can be produced as follows (...
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Ordinary kriging example step by step?

I have followed tutorials online for spatial kriging with both geoR and gstat (and also ...
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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 ...
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63 views

Are Kriging's residuals (i.e. $Z-\hat{Z}$) spatially independent?

Suppose data ${Z(s_i ):i=1, ..., n}$ are observed at spatial locations ${s_i :i=1, ..., n}$. To carry out the spatial prediction (predict un unknown $Z(s_0)$ at a known location $s_0$) we can use a ...
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217 views

Is a function describable by a Gaussian process smooth?

I understand that a stochastic process or function is considered a Gaussian process if sampling from it at any point some set of times yields a set of observations that match a Gaussian random ...
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94 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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What is the statistically correct way of performing the following interpolation?

I have a table with thousands of entries similar to the following: It is desired to determine Property 2 at the unknown locations. Property 1 and Property 2 are spatially correlated. By that I mean ...
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323 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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430 views

How do I estimate the prediction interval of back transformed log-normal data from Gaussian process?

I have some data that are clearly positively skewed and follow a log-normal distribution, lets assume the initial data is $Z = exp(Y)$, where $Y \sim N(\mu,\sigma^2)$. A Gaussian process assumes ...
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239 views

What is the difference between accounting for anisotropy and trend removal when performing Kriging?

Without being geostatistician, I read a bit about anisotropy detection, mostly from ArcGIS documentation and the R gstat package tutorial. But still, it is hard to have a confident understanding of ...
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What is 5th order kriging?

For our foray into geostatistics we got data that consists of measurements taken from the soil. The dataset has like concentrations of various different minerals. We were divided into a number of ...
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191 views

Kriging variance results

I'm quite a newb at statistics and interpolation, and I cannot understand how to interpret the error estimation computed by Kriging. For example, I performed kriging on temperature values (Celsius ...
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191 views

Determining covariance of irregularly spaced spatial data

I'm comparing concentration $C$ of a contaminant in the same spatial region at two time point 2000 and 2010 with sample size of $N_{2000}$ = 51 and $N_{2010}$ = 26 (not all the samples are from the ...
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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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what is the difference between Bayesian optimization and kriging?

Both methods use Gaussian process, and kriging uses the Best Linear Unbiased Predictor (BLUP) to predict the mean (this is not seen in Bayesian optimization?). At the bottom line, they also have ...
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Is kriging suitable for high dimensional regression problems?

I would like to point out that I am new to this field, so if I am not clear please forgive me (and correct me). I set up a DoE (Design of Experiment) with 11 inputs and 121 runs. I used a STOA (...
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Performing inference across multiple target variables with Gaussian Processes regression

Suppose I have a design matrix $\mathbf{X}$ with targets $\mathbf{y}_1$, when plotted looks like so: the data is very sparse, and the magnitude of the targets is shown by color bar, where each ...
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334 views

How to implement a Gaussian Markov Random field (GMRF) model in R?

I would like to model a (conditional) GMRF using a linear mixed effects model without having grid Data but only a neighbourhood matrix $W$. My model is given by $$Y=X\beta+ \epsilon$$ and the error ...
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Doubts on the methodology used for build and evaluate a Kriging model

I have run 3000 finite element (deterministic) simulations of a physical model, which has 10 design variables and one output variable. I have generated the sampling plan using the LH method. My ...
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Kriging with mean data instead of point data

Kriging is a technique to predict a realisation of a Gaussian process. The values of the realisation are known at a finite subset of points and we would like to optimally predict the values of the ...
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1answer
284 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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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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Universal Kriging

In universal kriging the general model is $$y(x)=h(x)^{t}\boldsymbol\beta + f(x)+\epsilon(x)$$ where $h(x)^{t}$ is a regression function such as $\left [1,x,x^{2} \right ]$ and $\boldsymbol\beta$ are ...
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129 views

Universal kriging with non-zero mean vector

Its is known that in ordinary Kriging (Gaussian Process) the mean and variance at any new point is given as $$\\\begin{pmatrix} \mathbf{y}\\y^{*} \end{pmatrix} \sim N(\mathbf{0},\begin{bmatrix} K &...
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206 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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730 views

Transformation of non-negative data including zeros

at first I want to mention that I am fully aware of this question here as well as the answers. Still, things won't work out as intended (using R). I have a lot of hourly rainfall data that include ...
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Why we krige residuals in regression-kriging?

Wikipedia says: In applied statistics, regression-kriging (RK) is a spatial prediction technique that combines a regression of the dependent variable on auxiliary variables (such as parameters ...
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Why likelihood based geostatistical modelling slower than non likelihood based counterpart

Likelihood based geo-statistics (geoR etc.) are usually slower than non-likelihood based geo-statistics (i.e. those based on just least square fitting, for example <...
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195 views

Spatial prediction on surface: very fine grid vs coarse grid + quick interpolation

Once I have fitted a spatial model (point-referenced data), I need to make a prediction map. A natural approach is to make prediction over a fine grid over the region. However, the required ...
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Is there a recursive version of Kriging or Inverse Distance spatial interpolation?

Classic use-case of Kriging: you have a 2d space, you have $n$ observations, each of them representing an exploratory dig. It has a $x$ and $y$ coordinate, and a $V$ representing the value discovered ...
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Help understanding a kriging variation for bare earth extraction

Problem: The authors of a paper (http://www.isprs.org/proceedings/XXXIV/part3/papers/paper106.pdf) develop a bare earth extraction algorithm for LiDAR that is based on kriging. What I don't ...
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1answer
412 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
290 views

Kriging with individual errors

When evaluating a Kriging prediction, it is possible to include a hyperparameter $\lambda$ to account for noise in the data. $\lambda$ can be estimated as a parameter in a maximum likelihood ...
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How to implement Kriging without x and y coordinates

I have some sample measurements taken from different locations. I want to predict the measurements in some surrounding locations that were not studies, for this I want to use Kriging. However, My ...
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How Does Kriging Interpolation work?

I am working on a problem in which I need to use Kriging to predict the value of some variables based on some surrounding variables. I want to implement its code by myself. So, I've went through too ...
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1answer
1k views

Gaussian process regression: leave-one-out prediction

According to Dubrule's Cross validation of kriging in a unique neighborhood, it is possible to compute leave-one-out the gaussian process prediction $\hat{Y}_{-i}(x_i)$ at a point $x_i$ from the ...
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516 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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1answer
121 views

Computing Issues with Kriging

I am having some issues with Kriging in R, and I was looking for some idea where I am going wrong. From what I can tell, I done a decent job removing the trend, and I believe my transformed data is ...
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2k views

Splines vs Gaussian Process Regression

I'm know that Gaussian Process Regression (GPR) is an alternative to using splines for fitting flexible nonlinear models. I would like to know in which situations would one be more suitable than the ...
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504 views

Kernel methods in machine learning?

I am beginning to tackle geostatistics problems where I tried to apply kriging(gaussian processes) to interpolate demographical water drop. According to my understanding, kernel methods are something ...
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Geostatistics: disaggregating regional data to subregions

I have been reading a lot on geostatistics. I am still unsure this problem falls under the umbrella of geostatistics, or if it is statistically feasible at all. I have the market share for a company ...
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How should I deal with non-normality in geostatistics?

I am working with two parameters, one is normally distributed the other is not. I have read several different books and articles with different opinions on what to do with non-normal data. Since ...