Sampling a Gaussian process with some observations (sampling the posterior), Matlab example

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 14:55

Summary:

This video discusses how to compute realizations of a stochastic process when you have observations of its value at a set of ‘measurement’ points. For example, the stochastic process may be the speed of each car at different points on a highway, and you want to ’interpolate’ for a specific car the most likely trajectories knowing that, in two positions where there was a radar, its recorded speeds were 110 and 80 km/h.

The first part of the video reviews previous concepts and best linear prediction, and discusses the code to generate a posterior mean and covariance matrix on a set of test points.

The second part of the video plots the confidence intervals of that posterior and generates various realizations (random functions) to illustrate the concept, using mvnrnd. The development is quite parallel to the video [gpsambEN], whose visualization is recommended prior to this one.

The final part of the video presents simulations of the results of changing the correlation distance in the covariance kernel.

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