zeta_est: Estimate of the normalization constant of the Riemann-Gauss...

In LauraMasiero/RiemannR: RiemannR - EEG-based BCI analysis with Riemannian geometry

Description

This function computes the normalization constant of the Riemann-Gauss distribution with simulations.

Usage

zeta_est(eta,n_channels,R)

Arguments

eta	a vector of numeric values (or a single real value) used to initialize the simulation. eta=-1/2*sigma^2
n_channels	a real number indicating the number of channels used in the EEG recordings.
R	Number of simulations.

Value

It returns a numeric vector (if the input eta was a vector, a number if eta was a real number) with the estimate of the normalization constant.

Author(s)

Laura Masiero, email: [e-mail]

References

Said, Salem, Lionel Bombrun, Yannick Berthoumieu e Jonathan Manton (2015). "Riemannian Gaussian Distributions on the Space of Symmetric Positive Definite Matrices". In: arXiv: 1507 . 01760. url: http://arxiv.org/abs/1507.01760.

Examples

values <- seq(1,2000)^2 #zeta(eta) simulation for a large sample
eta_values <- -10^6/values
zeta <- sapply(eta_values,zeta_est,n_channels=16,10000)
summary(log(zeta[3:2000]))
psi_smooth <- smooth.spline(eta_values[3:2000],log(zeta)[3:2000],nknots=1800) # function smoothing
logzetaprime <- predict(psi_smooth,der=1) # first derivative of psi

LauraMasiero/RiemannR documentation built on Sept. 29, 2020, 9:51 p.m.