In Craig44/stockassessmenthelper: Package to help plot stock assessment models and functionality

Surplus Production Models {#SPM}

This chapter will discuss some of the methods and functions available for simulating, estimating and visualising surplus production models [@polacheck1993fitting, @millar2000non].

The first section covers surplus production models, this will aid me getting used to state space models and learning Stan [@carpenter2017stan] and TMB [@tmb]. The first surplus production model framework has two sub models the process model (Equation \@ref(eq:processmodel) ) and the observation model (Equation \@ref(eq:observationmodel) ). We start with a simple biomass dynamics model as it is one of the simplest stock assessment models available \cite{hilborn1992quantitative}, and requires minimal data (catch history, relative/absolute index of abundance).

\begin{equation} B_{t+1} = f(B_t | \boldsymbol{\theta}) e^{\epsilon_{t,p} - 0.5\sigma^2_p} (#eq:processmodel) \end{equation}

\begin{equation} I_t = g(B_t | \boldsymbol{\theta}) e^{\epsilon_{t,o} - 0.5\sigma^2_o} (#eq:observationmodel) \end{equation}

x = 12;

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