Contents
What are Gaussian process models?
In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. every finite linear combination of them is normally distributed.
What is a GPR model?
Gaussian process regression (GPR) models are nonparametric kernel-based probabilistic models. You can train a GPR model using the fitrgp function.
What is a gaussian process Prior?
In short, a Gaussian Process prior is a prior over all functions f that are sufficiently smooth; data then “chooses” the best fitting functions from this prior, which are accessed through a new quantity, called “predictive posterior” or the “predictive distribution”.
Is there such a thing as Gaussian process regression?
Although the chapter is titled “Gaussian process regression”, and we’ll talk lots about Gaussian process surrogate modeling throughout this book, we’ll typically shorten that mouthful to Gaussian process (GP), or use “GP surrogate” for short. GPS would be confusing and GP SM is too scary.
How is the Gaussian process used in surrogate modeling?
Here the goal is humble on theoretical fronts, but fundamental in application. Our aim is to understand the Gaussian process (GP) as a prior over random functions, a posterior over functions given observed data, as a tool for spatial data modeling and surrogate modeling for computer experiments, and simply as a flexible nonparametric regression.
When does covariance decay in Gaussian process regression?
Here covariance decays exponentially fast as x and x ′ become farther apart in the input, or x -space. In this specification, observe that Σ(x, x) = 1 and Σ(x, x ′) < 1 for x ′ ≠ x. The function Σ(x, x ′) must be positive definite.
What do you call a Gaussian spatial modeling process?
Some call it kriging, which is a term that comes from geostatistics (Matheron 1963); some call it Gaussian spatial modeling or a Gaussian stochastic process. Both, if you squint at them the right way, have the acronym GaSP.