A comparison of statistical methods for fitting population models to data

A comparison was made of 3 statistical methods for fitting population models to abundance data: (1) Neyman-Pearson (frequentist), (2) Bayesian, and (3) Likelihood. Each school of statistical inference was briefly described, along with a description of the most common techniques used in each school for estimating the parameters of complex models, such as in fitting population models to abundance data. An example of each type of inference was shown by using the same data to estimate the depletion level of a population of spotted dolphins. The 3 specific techniques used were maximum likelihood estimation with a non-parametric bootstrap, approximation of the Bayesian posterior distribution using the sampling-importance-resampling numerical integration routine, and profile likelihood to represent likelihood inference for the parameter of interest. Point estimates from each technique were similar, but intervals varied substantially. Strengths and weaknesses of each approach were illustrated through the example.