Modeling the observations
$
\newcommand{\pcyipsii}{p_{y_i|\psi_i}}
\newcommand{\pcypsi}{p_{y|\psi}}
\newcommand{\bpsi}{\boldsymbol{\psi}}
\newcommand{\bu}{\boldsymbol{u}}
\newcommand{\bx}{\boldsymbol{x}}
\newcommand{\by}{\boldsymbol{y}}
\newcommand{\hazard}{h}
\newcommand{\std}[1]{\mbox{sd}\left(#1\right)}
\newcommand{\esp}[1]{\mathbb{E}\left(#1\right)}
\newcommand{\eqdef}{\mathop{=}\limits^{\mathrm{def}}}
\newcommand{\prob}[1]{ \mathbb{P}\!\left(#1\right)}
\newcommand{\probs}[2]{ \mathbb{P}_{#1}\!\left(#2\right)}
\newcommand{\Rset}{\mbox{$\mathbb{R}$}}
\newcommand{\Yr}{\mbox{$\mathcal{Y}$}}
\newcommand{\teps}{\tilde{\varepsilon}}
\newcommand{\like}{\cal L}
\newcommand{\pypsiij}{p_{y_{ij}|\psi_{i}}}
\newcommand{\ptypsiij}{p_{\transy(y_{ij})|\psi_{i}}}
\newcommand{\peps}{p_{\teps}}
\newcommand{\logit}{\rm logit}
\newcommand{\transy}{u}
\newcommand{\repy}{y^{(r)}}
\newcommand{\brepy}{\boldsymbol{y}^{(r)}}
$
Template:Extension \log S(t,\psi_i) &= & \hazard(t,\psi_i) \end{array}
\)
- Here, $\lambda(t,\psi_i) = \hazard(t,\psi_i)$ is known as the hazard function.
In summary, defining a model for the observations means choosing a (parametric) distribution. Then, a model must be chosen for the parameters of this distribution.
