Bernoulli distribution exponential family¶
\[Ber(x|\mu) = (1 - \mu) \exp[ x \log (\frac{\mu}{ 1 - \mu})] \]
\(\phi(x) = x\)
\(\theta = \log (\frac{\mu}{1 - \mu})\) this is the log odds ratio
\(Z = 1 / (1 - \mu)\)
We can recover the mean parameter \(\mu\) form the canonical form using:
\(\mu = sigm(\theta) = \frac{1}{1 + e^{-\theta}}\)