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.

Filter by
Sorted by
Tagged with
0 votes
0 answers
25 views

Distribution of the approximation error in Gaussian Process Regression (finite data setting)

I am learning about Gaussian Process Regression. I would like to have some references or results regarding the distribution of the error between a given function, and the posterior obtained in ...
user avatar
0 votes
0 answers
26 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 ...
user avatar
  • 111
1 vote
1 answer
23 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 ...
user avatar
  • 111
1 vote
0 answers
16 views

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) =...
user avatar
  • 11
-2 votes
0 answers
19 views

Kriging - Derivation of equations [duplicate]

While discussing about a problem, I told her about Kriging. My daughter asked me for the derivation of equations. Can you help me with derivation of Kriging Equations for Simple Kriging? (that can be ...
user avatar
8 votes
2 answers
1k views

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 ...
user avatar
  • 1,118
0 votes
0 answers
20 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?
user avatar
  • 11
0 votes
1 answer
21 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 ...
user avatar
  • 1
6 votes
1 answer
120 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 ...
user avatar
  • 5,013
0 votes
0 answers
17 views

Multicollinearity in regression kriging

I am doing regression kriging for a certain pollutant as a dependent variable, and for independent variables I'm using 4 variables that add to 100% for all observations. Because of this when I use ...
user avatar
1 vote
1 answer
85 views

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 ...
user avatar
0 votes
0 answers
70 views

gstat kriging vs. mgcv Gaussian process smooth

In Simon Wood's Generalized Additive Models: An Introduction with R, he states that the Gaussian process smooth (i.e., Gaussian process regression) is analogous to kriging. This is also stated on ...
user avatar
1 vote
1 answer
248 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 \...
user avatar
4 votes
1 answer
190 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 ...
user avatar
  • 140
1 vote
0 answers
136 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 ...
user avatar
1 vote
0 answers
97 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 ...
user avatar
1 vote
1 answer
226 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 ...
user avatar
3 votes
0 answers
446 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), ...
user avatar
  • 161
2 votes
0 answers
40 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 ...
user avatar
  • 556
1 vote
0 answers
55 views

(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 ...
user avatar
2 votes
1 answer
88 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)) ...
user avatar
1 vote
0 answers
82 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 ...
user avatar
  • 11
1 vote
0 answers
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 ...
user avatar
2 votes
1 answer
614 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 ...
user avatar
  • 1,261
1 vote
0 answers
22 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 ...
user avatar
  • 163
1 vote
0 answers
72 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 ...
user avatar
1 vote
1 answer
150 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 ...
user avatar
  • 143
2 votes
1 answer
376 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 ...
user avatar
  • 23
2 votes
0 answers
20 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 ...
user avatar
0 votes
0 answers
29 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?
user avatar
  • 1
0 votes
0 answers
124 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 ...
user avatar
1 vote
1 answer
162 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 ...
user avatar
  • 19.1k
0 votes
0 answers
64 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 ...
user avatar
1 vote
0 answers
88 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 ...
user avatar
  • 121
0 votes
1 answer
456 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: ...
user avatar
  • 101
1 vote
1 answer
212 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. ...
user avatar
  • 163
2 votes
0 answers
31 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 (...
user avatar
  • 885
10 votes
1 answer
5k views

Ordinary kriging example step by step?

I have followed tutorials online for spatial kriging with both geoR and gstat (and also ...
user avatar
  • 163
7 votes
2 answers
8k 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 ...
user avatar
1 vote
1 answer
82 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 ...
user avatar
2 votes
1 answer
1k 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 ...
user avatar
0 votes
1 answer
193 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 ...
user avatar
-1 votes
1 answer
36 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 ...
user avatar
1 vote
0 answers
575 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. ...
user avatar
  • 1,057
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 ...
user avatar
  • 61
1 vote
1 answer
647 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 ...
user avatar
  • 163
1 vote
0 answers
91 views

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 ...
user avatar
  • 305
2 votes
1 answer
351 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 ...
user avatar
2 votes
1 answer
238 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 ...
user avatar
  • 293
0 votes
0 answers
88 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 ...
user avatar
  • 305