pymc.HalfNormal#

class pymc.HalfNormal(name, *args, rng=None, dims=None, initval=None, observed=None, total_size=None, transform=UNSET, default_transform=UNSET, **kwargs)[source]#

Half-normal log-likelihood.

The pdf of this distribution is

\[ \begin{align}\begin{aligned}f(x \mid \tau) = \sqrt{\frac{2\tau}{\pi}} \exp\left(\frac{-x^2 \tau}{2}\right)\\f(x \mid \sigma) = \sqrt{\frac{2}{\pi\sigma^2}} \exp\left(\frac{-x^2}{2\sigma^2}\right)\end{aligned}\end{align} \]

Note

The parameters sigma/tau (\(\sigma\)/\(\tau\)) refer to the standard deviation/precision of the unfolded normal distribution, for the standard deviation of the half-normal distribution, see below. For the half-normal, they are just two parameterisation \(\sigma^2 \equiv \frac{1}{\tau}\) of a scale parameter.

(Source code, png, hires.png, pdf)

../../../_images/pymc-HalfNormal-1.png

Support

\(x \in [0, \infty)\)

Mean

\(\sqrt{\dfrac{2}{\tau \pi}}\) or \(\dfrac{\sigma \sqrt{2}}{\sqrt{\pi}}\)

Variance

\(\dfrac{1}{\tau}\left(1 - \dfrac{2}{\pi}\right)\) or \(\sigma^2\left(1 - \dfrac{2}{\pi}\right)\)
Parameters:
sigmatensor_like of float, optional

Scale parameter \(\sigma\) (sigma > 0) (only required if tau is not specified). Defaults to 1.

tautensor_like of float, optional

Precision \(\tau\) (tau > 0) (only required if sigma is not specified). Defaults to 1.

Examples

with pm.Model():
    x = pm.HalfNormal("x", sigma=10)

with pm.Model():
    x = pm.HalfNormal("x", tau=1 / 15)

Methods

HalfNormal.dist([sigma, tau])

Create a tensor variable corresponding to the cls distribution.