Information Matrix
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This collection of blogs is called Information Matrix, and it is named after an important quantity in statistics. If we are fitting a parametric model of the hazard rate, with log-likelihood:
\[ \ell( \alpha_1, \ldots, \alpha_n ) \]
as a function of \(n\) parameters \(\alpha_1, \ldots, \alpha_n\), then the information matrix is the matrix of second-order partial derivatives of \(\ell\). That is, the matrix \({\cal I}\) with \(ij\)th component: