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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 deal with seasonality in spatio-temporal kriging?

I'm currently working with a spatio temporal dataset of PM10 in North Italy, I have 4 years of weekly data and 160 stations on the region. I seasonally adjusted the time series of each station one by ...
Giovanni's user avatar
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19 views

Can kriging method be used for dataset that is not spatial?

Sorry if the question sounds stupid. I am new to this. Consider the following dataset: ...
Amisha Dhimal's user avatar
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Kriging : when it is said kriging is an unbiaised estimator, is that synonymous with saying it is an exact interpolator?

I feel like they are not synonymous, but I cannot intuitively explain the difference between "unbiased" and "exact." In other words, I am asking about the difference between the ...
user386309's user avatar
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Covariance estimation in simple kriging: the "dead end" problem (authorization of using variogram)

I am confused about the presentation of using variogram in simple kriging in the book of Multivariate geostatistics by H. Wackernagel (1995). I understand the process of derivation of simple kriging ...
hamsa's user avatar
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6 votes
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371 views

Lipschitzness of posterior mean of Gaussian process?

Let $T$ be a compact set, and let $K \colon T \times T \to \mathbb{R}$ be a positive definite kernel. Consider the canonical pseudo-distance $$d_K(x,y) = \sqrt{K(x,x) + K(y,y) - 2 K(x,y)}.$$ Let $f$ ...
ccriscitiello's user avatar
1 vote
1 answer
124 views

Declustering spatial data and kriging

I am doing a simple project on a mining dataset and came across some problems: Should I use the declustered values to model the variogram? Do I apply ordinary kriging to the original or to the ...
Gustavo Scholze's user avatar
1 vote
0 answers
152 views

Gaussian Process as a time series model, pros and cons

When talkin' about time series models, ARIMA, SARIMAX, Prophet or VAR is what mostly is on the table. But what would the benefit be of using a Gaussian Process Regressor instead, in which situations ...
Henri's user avatar
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Posterior covariance of the function values and derivatives of a Gaussian Process

I'm trying to figure out how to calculate the cross-terms of the covariance matrix between the function values and derivatives of a Gaussian Process. For context, this is needed for Gaussian Process ...
Eddy's user avatar
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65 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
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1 vote
1 answer
85 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
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1 vote
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How to constrain ordinary kriging weights to sum to 1 in R

I need to perform ordinary kriging on a dataset and I understand that I need the weights to sum to 1, I just don't understand how to set that up properly. For example, my covariance function is C(h) =...
Ric's user avatar
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10 votes
2 answers
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Estimating probability of attack in Ukraine, given count data

I was looking at some attack count data in Ukraine for different days. The data is gathered from the ACCLED dataset, and there is a picture below. The picture shows individual attacks, but I can apply ...
krishnab's user avatar
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42 views

Is there a Sequential Gaussian Simulation that uses Ordinary Kriging?

As far as I have read, Sequential Gaussian Simulation always uses Simple Kriging. Is there any chance that it uses Ordinary Kriging?
Dara's user avatar
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55 views

Kriging with positivity constraint using the STK toolbox

I work in the aerospace world, specifically doing calibration and characterization of detectors and space instruments (cubesats, space spectrographic satellites etc.) We always need to interpolate our ...
SLC's user avatar
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8 votes
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560 views

What is the difference between a non-zero nugget and a noise term in Kriging/GPR?

With some Gaussian Process Regression/Kriging models, it's possible to specify both a non-zero nugget, and a noise term. For example, in Scikit-learn's GPR model, there is an ...
naught101's user avatar
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2 votes
1 answer
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Analytical Leave-one-out prediction variance for Kriging

I make extensive use of Kriging (Gaussian Process regression) methods in my work especially using the leave-one-out error calculation that you can get from the Gram matrix. Background: To compute the ...
Justin Winokur's user avatar
1 vote
1 answer
634 views

How can concentrated (profile) log marginal likelihood be used to optimize the mean and scale(outputscale) parameters in Gaussian Process Regression?

The log marginal likelihood which is used in Gaussian Process Regression comes from a Multivariate Normal pdf Gaussian Processes for Machine Learning, p.19, eqn. 2.30, Surrogates, Chapter 5, eqn. 5.4 \...
m-julian's user avatar
4 votes
1 answer
533 views

Who first proposed Bayesian optimisation with Gaussian processes?

From what I understand, the 'standard' approach to Bayesian Optimisation uses a Gaussian process for the prior (as opposed to more recent proposals like TPE or Bayesian Optimisation with random ...
oulenz's user avatar
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258 views

Interpreting a Distance & Time 3D Variogram for Variogram modeling

I am trying to understand some concepts of variograms. I have made several variogram models in R and am trying to understand exactly what they mean. My data is ...
Coldchain9's user avatar
1 vote
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222 views

Variogram fit in R not converging

I have taken a shapefile from Open NYC Data and performed the following method. My end goal is to predict Taxi trip_duration at various points across the city of ...
Coldchain9's user avatar
1 vote
1 answer
676 views

Cokriging and collocated cokriging data requirements

In this wiki article and elsewhere in educational materials/papers, I have seen people refer to the idea that secondary data, if used (appropriately) in cokriging or collocated cokriging, is usually ...
Denys D.'s user avatar
4 votes
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1k views

Differences between Kriging and Gaussian Process Regression

I am having quite difficult time to clearly understand the differences between Kriging and Gaussian Process Regression. Here is what I have understood so far: For simple kriging (mean value known), ...
Akusa's user avatar
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2 votes
0 answers
149 views

Conditional distribution of Ornstein-Uhlenbeck on two fixed points

The conditional distribution of a Ornstein-Uhlenbeck $X(t)$ conditional on $X(0)$ is given by $$ X(t)|X(0) = X(0)e^{-t} + \mu(1 - e^{-t}) $$ This process is usually only defined for $t>0$ (future ...
Frank Vel's user avatar
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(Co)kriging / co-located kriging with heterogenous measurement errors

I have a large set of polygons on a map, some of which contain data on 2 count variables, say ($z_{1}$ and $z_{2}$) that are correlated. In fact, $z_{2}$ most likely causes $z_{1}$ without the ...
Denys D.'s user avatar
3 votes
1 answer
135 views

Intuition Behind Correlation Function in Kriging Models

I'm thinking and researching extensively to interpret the parameter $\theta$ (activeness parameter) in Gaussian correlation function in a Kriging model, namely as: $$ K(h;\theta)=exp(-h^2/(2\theta^2)) ...
user273192's user avatar
1 vote
0 answers
165 views

Intuitive explanation of Gaussian Process Regression

How would you intuitively explain the idea behind Gaussian Process Regression to someone unfamiliar with stochastic processes? Especially the point where you discuss modeling covariance, choice of ...
Antonis's user avatar
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1 vote
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28 views

“Jumping” among several interpolation techniques?

I am comparing several interpolation methods using monthly climatic data, through RMSE and a 10-fold cross-validation scheme. What I'm observing is that the performances vary from one month to ...
perep1972's user avatar
5 votes
1 answer
1k views

Modeling trends with Gaussian Processes

I am trying to use Gaussian Process Regression to model data that has a clear upward rising trend. Here is a basic plot of the data - The most well-known example of the flexibility of GPs in such ...
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1 vote
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27 views

learning time series by machine learning

I am trying to learn a mapping between coordinates x,y,z,d, with d=sqrt(x**2 + y**2 + z**2), and a scalar. Each ...
johnhenry's user avatar
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91 views

When regularizing based on an informative prior, how to give model a little more freedom to partially reject regulariziation

I am new here I hope this question is appropriate. I am modelling a spatial domain, whereby I have repeated measures at n locations. I make a bayesian linear model at each n locations based on about ...
MindtheData's user avatar
1 vote
1 answer
319 views

Can I replace the distribution in Gaussian Process Regression with a different regression?

Sorry for the confusing title. Let me try to clarify: I have a time series of wind speeds with some missing points here and there. I want to interpolate these points and have tried mainly polynomial ...
kushy's user avatar
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2 votes
1 answer
536 views

Is the spherical covariance function not positive definite for d > 3?

I read in a textbook (Japanese one) that the spherical covariance function is only valid for dimensions $d = 1,$ $2,$ and $3.$ I have the following questions: Does that mean the spherical covariance ...
Jiro's user avatar
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2 votes
0 answers
24 views

Cokriging variances differ using cross validation

I'm investigating cokriging using various metals in the Meuse dataset but the variances output by R when I predict values at gridded points differ substantially from the variances produced by cross ...
Ben Collister's user avatar
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32 views

Why do you need a variogram for Kriging? goldingn/gpe package?

I am using golingn/gpe (github) package, and it does not provide a variogram and instead look at co-variances. Is it possible to do kriging without providing variograms?
XiygX's user avatar
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0 answers
287 views

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 ...
Patrick Balada's user avatar
1 vote
1 answer
208 views

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 ...
Kodiologist's user avatar
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73 views

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 ...
Kristóf Marussy's user avatar
1 vote
0 answers
171 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 ...
Yollanda Beetroot's user avatar
0 votes
1 answer
893 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: ...
Jason's user avatar
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3 votes
1 answer
281 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. ...
Pigna's user avatar
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2 votes
0 answers
32 views

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 (...
egg's user avatar
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10 votes
1 answer
7k views

Ordinary kriging example step by step?

I have followed tutorials online for spatial kriging with both geoR and gstat (and also ...
Pigna's user avatar
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7 votes
2 answers
11k 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 ...
MachineEpsilon's user avatar
1 vote
1 answer
107 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 ...
A. Tavassoli's user avatar
2 votes
1 answer
2k 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 ...
Pavel Komarov's user avatar
0 votes
1 answer
337 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 ...
Ali Jamali's user avatar
-1 votes
1 answer
41 views

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 ...
Ali Jamali's user avatar
1 vote
0 answers
820 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. ...
compbiostats's user avatar
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3 votes
0 answers
1k 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 ...
Mahshrp's user avatar
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1 vote
1 answer
983 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 ...
Delforge's user avatar
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