Kalman_smoother: the predictive mean and predictive variance by Kalman...

In FastGaSP: Fast and Exact Computation of Gaussian Stochastic Process

Description

This function computes the predictive mean and predictive variance on the sorted input and testing input by the Kalman Smoother.

Usage

Kalman_smoother(param,have_noise,index_obs,delta_x_all,output,sigma_2_hat,kernel_type)

Arguments

param	a vector of parameters. The first parameter is the natural logarithm of the inverse range parameter in the kernel function. If the data contain noise, the second parameter is the logarithm of the nugget-variance ratio parameter.
have_noise	a bool value. If it is true, it means the model contains a noise.
index_obs	a vector where the entries with 1 have observations and entries with 0 have no observation.
delta_x_all	a vector for the differences between the sorted input and testing input locations.
output	a vector with dimension num_obs x 1 for the observations at the sorted input locations.
sigma_2_hat	a numerical value of variance parameter of the covariance function.
kernel_type	A character specifying the type of kernel.

Value

A list where the first item is the the predictive mean and the second item is predictive variance on the sorted input and testing input by the Kalman Smoother.

Author(s)

Mengyang Gu [aut, cre]

Maintainer: Mengyang Gu <[e-mail]>

References

Hartikainen, J. and Sarkka, S. (2010). Kalman filtering and smoothing solutions to temporal gaussian process regression models, Machine Learning for Signal Processing (MLSP), 2010 IEEE International Workshop, 379-384.

M. Gu, Y. Xu (2017), Nonseparable Gaussian stochastic process: a unified view and computational strategy, arXiv:1711.11501.

M. Gu, X. Wang and J.O. Berger (2018), Robust Gaussian Stochastic Process Emulation, Annals of Statistics, 46, 3038-3066.

See Also

predict for more details about the prediction on the testing input by the Fast GaSP class.

FastGaSP documentation built on Sept. 5, 2021, 5:36 p.m.