Statistical Analysis of the Ricker Model

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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)(-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)(-N(t)+ε(t+1)) and what is observed at time t is a Poisson random variable with parameter φN(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.