pymc.HalfNormal — PyMC 5.22.0 documentation (original) (raw)
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 distribution.
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)
| 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. |
|---|