Statistical Analysis of the Ricker Model

Abstract

The Ricker model was introduced in the context of managing fishing stocks. It is a discrete non-linear iterative model given by $N(t+1)=rN(t)\exp(-N(t))$ where $N(t)$ is the population at time $t$. The model treated in this paper includes a random component $N(t+1)=rN(t)\exp(-N(t)+\varepsilon(t+1))$ and what is observed at time $t$ is a Poisson random variable with parameter $\varphi N(t)$. Such a model has been analysed using `synthetic likelihood' and ABC (Approximate Bayesian Computation). In contrast this paper takes a non-likelihood approach and treats the model in a consistent manner as an approximation. The goal is to specify those parameter values if any which are consistent with the data.