My covariance function looks like this:
A simpler example, where the problem of an ill-defined inverse arises, is
\Sigma(t,t') = \exp(-(t-t')^2)
If one could understand why this fails in contrast to e.g.
\Sigma(t,t') = \exp(-|t-t'|) or \Sigma(t,t') = 1-|t-t'|
where the inverse exists...
Thank you, the process is indeed a Gaussian process. I have defined my mean μ(t) and the covariance function Σ(t,t') as functions of the continuous time variables t and t'.
This, however, does allow me to construct a probability density P(x(t)) for the continuous time series x(t) (which would...
Hello everyone,
I am currently considering a set of random variables, \vec{x} = [x_1,x_2,...x_N] which are know to follow a multivariate normal distribution,
P(\vec{x}) \propto \mathrm{exp}(-\frac{1}{2}(\vec{x}-\vec{\mu})^\mathrm{T}\Sigma^{-1}(\vec{x}-\vec{\mu}))
The covariance matrix Σ and...