Ordinary kriging is a BLUP for random fields, but linear estimation results are often not optimal when there is a nonlinear relationship between random fields and the index set. Analytic kriging generalizes the weight coefficients in ordinary kriging to functions, thus enabling nonlinear estimation of random fields. Most commonly, given an indicator function, analytic kriging is also known as indicator kriging.

Ordinary kriging is a linear estimation system for any intrinsically smooth random field that satisfies the isotropic assumption. In an inherently smooth random field under isotropic assumptions, the mathematical expectation is independent of its location and the covariance is only a function of the distance between points. The covariance function of the random field is usually unknown and needs to be approximated by the variance function, which is also only related to the distance between points. Since the mathematical expectation of the intrinsically smooth random field is equal everywhere, simple kriging itself satisfies the BLUP condition and is easy to solve for its kriging weights.

The method performs spatial distribution studies with the ability to fuse multiple aspects of data of different precision and quality, and divides these data into two aspects: (i) specialized data (KS): data that represent data related to the study area, including hard and soft data; (ii) universal knowledge/data (KG): data or knowledge used to describe the overall characteristics of the spatial random domain, such as general natural laws, empirical knowledge and hard data based on any order of statistical kinetic differences (e.g., mathematical expectation, covariance, variance, etc.). Based on these two aspects of data, the BME method is divided into two steps: (i) using KG, based on the maximum entropy principle, calculate the prior probability density function (pdf) of the distribution of unmeasured variables in the study area; (ii) using KS, based on Bayesian conditional probability, update the prior pdf obtained in the previous step to obtain the Based on the final posterior pdf, a variety of plots can be easily produced, such as prediction plots, probability distribution plots beyond a certain threshold, etc.

GSLPE is a least power estimation based on geostatistics (Ordinary Kriging, etc.) and generalized Gaussian distribution. GSLPE has good accuracy, stability and robustness for the disorganized measurements with spatial heterogeneity, and is customized to the studies on upscaling for multi-point measurements.

Installation: no installation required;

The third-party toolkit: LAPACK、IT++、armadillo

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CKT is a cokriging algorithm in conjunction with truncated power variogram, which has the ability to represent multiscale overlapping random fields. CKT specializes in capturing the multi-scale behavior of a geophysical variable ranging from the point scale to large windows, and its estimates are explicitly related to the magnitude of the scale. CKT performs better in a heavy-tailed distribution.

Installation :no installation required;

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If the covariance functions are of equivalent form and the modeled objects are smoothGaussian process，The ordinary kriging output has the sameaverage and confidence interval as the Gaussian Process Regression（GPR）output under normal likelihood.，with stable predictive effect^[2][1]。The Kriegin method is a typical geostatistical algorithm that is applied toGeosciences、Environmental Science、Atmospheric Sciencesand other fields^[1].

Regression kriging is a combination of the Generalized Linear Model (GLM) and kriging, and is the most common hybrid algorithm. Regression kriging first uses the GLM to estimate the determinstic effect in the spatial field, and then uses kriging to estimate the random field consisting of regression residuals.

The multi-point geostatistics algorithm becomes a truly practical stochastic modeling algorithm. The traditional two-point geostatistics stochastic modeling method can only consider the correlation between two points in space, while multi-point geostatistics focuses on expressing the correlation between multiple points, which overcomes the shortage of two-point geostatistics and is the current international frontier research direction. Multi-point geostatistics is relative to the traditional two-point geostatistics, which can reflect the geometry and mutual coordination relationship of multiple points in space, and has a greater advantage in modeling the distribution of complex-shaped geological bodies.

Simple kriging is mathematically the simplest, but the least general.It assumes the expectation of the random field to be known.

Installation: online;

Dependent libraries: gstat ;

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The random field can be modeled using pan-Kriging when it is known that the random field is a superposition of various homogeneous intrinsically smooth processes and drift quantities. Pan-Kriging assumes that the drift is a linear combination of a series of known analytic functions.