Sampling a Gaussian process (realizations), Matlab example

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 13:57

Summary:

This video discusses how to compute ‘realizations’ (random functions $f(x)$) of a Gaussian stochastic process with given mean function $\overline{f}(x)$ and covariance kernel $k(x_1,x_2)$. As the process is ’continuous time’, samples of it will only be generated in a finite set of test points.

The video discusses the code to generate the covariance matrix in said set of test points, the meaning of the chosen stationary covariance kernel (quadratic exponential, but it can be any other), the band-type structure of the covariance matrix and the use of mvnrnd to generate the process realizations. The internal detail of the mvnrnd command requires carrying out diagonalization or Cholesky decomposition of the covariance matrix, but those implementation details are out of the scope of this video.

To better understand this type of processes, the correlation abscissa distance parameter is changed in the covariance function, also, in an additional example, white measurement noise is added (increasing the diagonal of the covariance), etc.

The video [gpsambpoEN], a continuation of this one, will discuss the same problem (generating realizations) when observations are available at some ‘measurement’ points of the value of the process.

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.