class revrand.likelihoods.Poisson(tranfcn='exp')

A Poisson likelihood, useful for various Poisson process tasks.

An exponential transformation function and a softplus transformation function have been implemented.

\[p(y_i | f_i) = \frac{g(f_i)^{y_i} e^{-g(f_i)}}{y_i!}\]

where \(y_i\) is a target, \(f_i\) the value of the latent function corresponding to the target, and \(g(\cdot)\) is the tranformation function, which can be either an exponential function, or a softplus function (\(\log(1 + \exp(f_i)\)).

Parameters:tranfcn (string, optional) – this may be ‘exp’ for an exponential transformation function, or ‘softplus’ for a softplut transformation function.

See class docstring.


Ey(f) Expected value of the Poisson likelihood.
__init__([tranfcn]) See class docstring.
cdf(y, f) Cumulative density function of the likelihood.
df(y, f) Derivative of Poisson log likelihood w.r.t. f.
dp(y, f, *args) Derivative of Bernoulli log likelihood w.r.t.the parameters, \(\theta\).
loglike(y, f) Poisson log likelihood.


params Get this object’s Parameter types.