Related papers: Explaining and Connecting Kriging with Gaussian Pr…
Kriging is a widely recognized method for making spatial predictions. On the sphere, popular methods such as ordinary kriging assume that the spatial process is intrinsically homogeneous. However, intrinsic homogeneity is too strict in many…
This article proposes a new kriging that has a rational form. It is shown that the generalized least squares estimate of the mean from rational kriging is much more well behaved than that from ordinary kriging. Parameter estimation and…
To obtain more accurate model parameters and improve prediction accuracy, we proposed a regularized Kriging model that penalizes the hyperparameter theta in the Gaussian stochastic process, termed the Theta-regularized Kriging. We derived…
Gaussian process (GP) models are effective non-linear models for numerous scientific applications. However, computation of their hyperparameters can be difficult when there is a large number of training observations (n) due to the O(n^3)…
We propose a method with better predictions at extreme values than the standard method of Kriging. We construct our predictor in two ways: by penalizing the mean squared error through conditional bias and by penalizing the conditional…
Analyzing massive spatial datasets using Gaussian process model poses computational challenges. This is a problem prevailing heavily in applications such as environmental modeling, ecology, forestry and environmental heath. We present a…
Approximation of functions satisfying partial differential equations (PDEs) is paramount for simulation of physical fluid flows and other problems in physics. Recently, physics-informed machine learning approaches have proven useful as a…
In this paper, we investigate Gaussian process regression models where inputs are subject to measurement error. In spatial statistics, input measurement errors occur when the geographical locations of observed data are not known exactly.…
Treeging combines the flexible mean structure of regression trees with the covariance-based prediction strategy of kriging into the base learner of an ensemble prediction algorithm. In so doing, it combines the strengths of the two primary…
Gaussian process fitting, or kriging, is often used to create a model from a set of data. Many available software packages do this, but we show that very different results can be obtained from different packages even when using the same…
Within the past two decades, Gaussian process regression has been increasingly used for modeling dynamical systems due to some beneficial properties such as the bias variance trade-off and the strong connection to Bayesian mathematics. As…
Computer simulation has become the standard tool in many engineering fields for designing and optimizing systems, as well as for assessing their reliability. To cope with demanding analysis such as optimization and reliability, surrogate…
Network service providers and customers are often concerned with aggregate performance measures that span multiple network paths. Unfortunately, forming such network-wide measures can be difficult, due to the issues of scale involved. In…
Spatial prediction is a fundamental task in geography. In recent years, with advances in geospatial artificial intelligence (GeoAI), numerous models have been developed to improve the accuracy of geographic variable predictions. Beyond…
Gaussian process models -also called Kriging models- are often used as mathematical approximations of expensive experiments. However, the number of observation required for building an emulator becomes unrealistic when using classical…
Spatial prediction in an arbitrary location, based on a spatial set of observations, is usually performed by Kriging, being the best linear unbiased predictor (BLUP) in a least-square sense. In order to predict a continuous surface over a…
The computational effort for the evaluation of numerical simulations based on e.g. the finite-element method is high. Metamodels can be utilized to create a low-cost alternative. However the number of required samples for the creation of a…
The main aim of applied geostatistics is to derive `mean' and `variance' of ore to the practicing miner. This paper suggests brand-new approach to the problem.
Kriging (or Gaussian process regression) is a popular machine learning method for its flexibility and closed-form prediction expressions. However, one of the key challenges in applying kriging to engineering systems is that the available…
There are various methods to analyze different kinds of data sets. Spatial data is defined when data is dependent on each other based on their respective locations. Spline and Kriging are two methods for interpolating and predicting spatial…