Fisherian or Bayesian methods of integrating diverse statistical information?

Abstract

Listen

Translate article

Directly observed data are in many cases combined with diverse indirect information to draw inference on parameters of interest to the fishery scientist. The indirect information might be based on previous data, analogous data or the researcher's expert judgement. The Bayesian prior distribution is the most common concept for representing such indirect information, and the Bayesian paradigm is gaining popularity. An alternative methodology based on the likelihood principle is presented and compared to the Bayesian. In the tradition of R.A. Fisher, the method concentrates on the likelihood function, without bringing in prior distributions that are not based on data. To provide for the integration of relevant indirect statistical information into the likelihood function, the concept of indirect likelihood is proposed. The indirect likelihood is treated as an ordinary independent component of the likelihood. If the indirect likelihood of a parameter is based on previous data, the inclusion of the indirect likelihood in the new study amounts to combining the old and the new data. The two methods are explained and compared, and it is argued that the likelihood method often is advantageous in the scientific context.