Get_log_det_S2: the natural logarithm of the determinant of the correlation...

In FastGaSP: Fast and Exact Computation of Gaussian Stochastic Process

the natural logarithm of the determinant of the correlation matrix and the estimated sum of squares in the exponent of the profile likelihood

Description

This function computes the natural logarithm of the determinant of the correlation matrix and the estimated sum of squares for computing the profile likelihood.

Usage

Get_log_det_S2(param,have_noise,delta_x,output,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.
delta_x	a vector with dimension (num_obs-1) x 1 for the differences between the sorted input locations.
output	a vector with dimension num_obs x 1 for the observations at the sorted input locations.
kernel_type	A character specifying the type of kernel.

Value

A list where the first value is the natural logarithm of the determinant of the correlation matrix and the second value is the estimated sum of squares.

Author(s)

Mengyang Gu [aut, cre], Xinyi Fang [aut], Yizi Lin [aut]

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

log_lik for more details about the profile likelihood.

FastGaSP documentation built on April 4, 2025, 5:16 a.m.