class revrand.likelihoods.Gaussian(var=Parameter(value=1.0, bounds=Positive(upper=None), shape=()))

A univariate Gaussian likelihood for general regression tasks.

No transformation function is needed since this is (conditionally) conjugate to the GLM prior.

\[p(y_i | f_i) = \frac{1}{\sqrt{2 \pi \sigma^2}} \exp\left(- \frac{(y_i - f_i)^2}{2 \sigma^2} \right)\]

where \(y_i\) is a target, \(f_i\) the value of the latent function corresponding to the target and \(\sigma\) is the observation noise (standard deviation).

Parameters:var (Parameter, optional) – A scalar Parameter describing the initial point and bounds for an optimiser to learn the variance parameter of this object.
__init__(var=Parameter(value=1.0, bounds=Positive(upper=None), shape=()))

See class docstring.


Ey(f, var) Expected value of the Gaussian likelihood.
__init__([var, bounds, shape]) See class docstring.
cdf(y, f, var) Cumulative density function of the likelihood.
df(y, f, var) Derivative of Gaussian log likelihood w.r.t. f.
dp(y, f, var) Derivative of Gaussian log likelihood w.r.t.the variance \(\sigma^2\).
loglike(y, f[, var]) Gaussian log likelihood.


params Get this object’s Parameter types.