Best practices for the provision of prior information for Bayesian stock assessment.

Abstract

This manual represents a review of the potential sources and methods to be applied when providing prior information to Bayesian stock assessments and marine risk analysis. The manual is compiled as a product of the EC Framework 7 ECOKNOWS project (www.ecoknows.eu). The manual begins by introducing the basic concepts of Bayesian inference and the role of prior information in the inference. Bayesian analysis is a mathematical formalization of a sequential learning process in a probabilistic rationale. Prior information (also called ”prior knowledge”, ”prior belief”, or simply a ”prior”) refers to any existing relevant knowledge available before the analysis of the newest observations (data) and the information included in them. Prior information is input to a Bayesian statistical analysis in the form of a probability distribution (a prior distribution) that summarizes beliefs about the parameter concerned in terms of relative support for different values. Apart from specifying probable parameter values, prior information also defines how the data are related to the phenomenon being studied, i.e. the model structure. Prior information should reflect the different degrees of knowledge about different parameters and the interrelationships among them. Different sources of prior information are described as well as the particularities important for their successful utilization. The sources of prior information are classified into four main categories: (i) primary data, (ii) literature, (iii) online databases, and (iv) experts. This categorization is somewhat synthetic, but is useful for structuring the process of deriving a prior and for acknowledging different aspects of it. A hierarchy is proposed in which sources of prior information are ranked according to their proximity to the primary observations, so that use of raw data is preferred where possible. This hierarchy is reflected in the types of methods that might be suitable – for example, hierarchical analysis and meta-analysis approaches are powerful, but typically require larger numbers of observations than other methods. In establishing an informative prior distribution for a variable or parameter from ancillary raw data, several steps should be followed. These include the choice of the frequency distribution of observations which also determines the shape of prior distribution, the choice of the way in which a dataset is used to construct a prior, and the consideration related to whether one or several datasets are used. Explicitly modelling correlations between parameters in a hierarchical model can allow more effective use of the available information or more knowledge with the same data. Checking the literature is advised as the next approach. Stock assessment would gain much from the inclusion of prior information derived from the literature and from literature compilers such as FishBase (www.fishbase.org), especially in data-limited situations. The reader is guided through the process of obtaining priors for length–weight, growth, and mortality parameters from FishBase. Expert opinion lends itself to data-limited situations and can be used even in cases where observations are not available. Several expert elicitation tools are introduced for guiding experts through the process of expressing their beliefs and for extracting numerical priors about variables of interest, such as stock–recruitment dynamics, natural mortality, maturation, and the selectivity of fishing gears. Elicitation of parameter values is not the only task where experts play an important role; they also can describe the process to be modelled as a whole. Information sources and methods are not mutually exclusive, so some combination may be used in deriving a prior distribution. Whichever source(s) and method(s) are chosen, it is important to remember that the same data should not be used twice. If the plan is to use the data in the analysis for which the prior distribution is needed, then the same data cannot be used in formulating the prior. The techniques studied and proposed in this manual can be further elaborated and fine-tuned. New developments in technology can potentially be explored to find novel ways of forming prior distributions from different sources of information. Future research efforts should also be targeted at the philosophy and practices of model building based on existing prior information. Stock assessments that explicitly account for model uncertainty are still rare, and improving the methodology in this direction is an important avenue for future research. More research is also needed to make Bayesian analysis of non-parametric models more accessible in practice. Since Bayesian stock assessment models (like all other assessment models) are made from existing knowledge held by human beings, prior distributions for parameters and model structures may play a key role in the processes of collectively building and reviewing those models with stakeholders. Research on the theory and practice of these processes will be needed in the future.