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