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\section*{Log-normal model for Stochastic volatility}

\subsection*{Parametrization}

The likelihood is
\[
y_i |\ldots \;\sim\; N(c - \frac{1}{2} \sigma^{2}_i, \sigma^{2}_i)
\]
where the mean depends on the variance, and $c$ is an optional
hyperparameter.

\subsection*{Link-function}

The variance is linked to the linear predictor as
$\eta_i$ as:
\[
\log (\sigma^{2}_i) = \eta_i
\]

\subsection*{Hyperparameters}

This likelihood has one hyperparmeter
\begin{displaymath}
    \theta = c
\end{displaymath}
and the prior is defined on $\theta$. By default, $c$ is fixed to $c=0$.

\subsection*{Specification}

\begin{itemize}
\item \texttt{family="stochvolln"}
\end{itemize}

\subsubsection*{Hyperparameter spesification and default values}
\input{../hyper/likelihood/stochvolln.tex}

\subsection*{Example}
\verbatiminput{example-stochvolln.R}

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