1.3 The definition of bayesian estimation

\[w \in W \mapto \prod_{i=1}^{n} p(X_{i} \mid w) .\] \[w_{ML} := \arg\max_{w \in W} p(X_{i} \mid w) .\]

$w_{ML}$ is called maximum lilelihood estimator. If we use $\hat{p}(x) := p(x \mid w_{ML})$ for prediction

\[\frac{ Z_{n}(\beta) }{ \phi(w) \prod_{i=1}^{n} p(X_{i} \mid w)^{\beta} } = \int_{W} \phi(w^{\prime}) \frac{ \phi(w) }{ iiiii\phi(w) } \ dw^{\prime}\]