Solution
= Solution
For log-likelihood $\ell(\beta;Y)$, the <score function> and <Fisher information matrix> are
$$
U(\beta)=\nabla_\beta\ell(\beta;Y),
\qquad
\mathcal I(\beta)
=-\mathbb E_\beta[\nabla_\beta^2\ell(\beta;Y)]
=\operatorname{cov}_\beta(U(\beta)).
$$
The <Fisher scoring> iteration replaces the observed Hessian in Newton's method by its expectation:
$$
\boxed{\beta^{(m+1)}
=\beta^{(m)}
+\mathcal I(\beta^{(m)})^{-1}U(\beta^{(m)})}.
$$