5.1 Why use Bayesian methods?

5.2 Overcoming problems with prior distributions

5.3 The computational demands

5.4 In conclusion

The main reason for using a Bayesian approach to stock assessment is that it facilitates representing and taking fuller account of the uncertainties related to models and parameter values. In contrast, most decision analyses based on maximum likelihood (or least squares) estimation involve fixing the values of parameters that may, in actuality, have an important bearing on the final outcome of the analysis and for which there is considerable uncertainty. One of the major benefits of the Bayesian approach is the ability to incorporate prior information. While other stock assessment approaches use "prior" information by specifying levels or ranges of individual parameters for use in sensitivity analysis, the Bayesian approach forces the analyst to look at historical data sets or to canvass expert knowledge to determine what is known about the biological parameters and processes. Most traditional stock assessment methods do not use any of the quantitative information that could be gathered from historical experience with other stocks and, in effect, treat each stock assessment as a new and independent problem.

In the past, the effects of uncertainty have been evaluated through sensitivity analysis. In general, this involved changing the value of a single parameter only and rerunning the entire stock assessment. This limitation to a single parameter was due to time-constraints and to avoid large amounts of model output. There is clearly a need for sensitivity analysis for any stock assessment. However, current practice cannot guarantee that some (reasonably plausible) combination of parameter values does not give rise to behaviour that would not be expected from the results of sensitivity tests that involve changing the value of a single parameter only. In addition, it is often difficult to summarise the management implications of sensitivity tests that exhibit considerable sensitivity without some form of integration across those tests. In contrast, the Bayesian approach to stock assessment explicitly allows for weighting across alternative hypotheses through Bayes Theorem. The use of Bayesian techniques does not eliminate the need for sensitivity tests. It is still necessary to conduct an extensive examination of the sensitivity of the stock assessment and decision analysis results to the choice of the prior distributions, which data sets to include in the assessment which to ignore, etc. Current stock assessments, both Bayesian and non-Bayesian, tend to ignore the true range of uncertainty (both model and parameter). In particular, model-structure uncertainty is usually completely ignored (Sainsbury (1988) is a notable exception) even though the impact of this source of uncertainty can be more important than that of uncertainty about the values for the parameters for any one model.

The reasons for not considering the full range of uncertainty were discussed before (see Section 1.2.1) but briefly these relate to lack of knowledge about which alternative models to consider, computational constraints and time limitations. Our experience is that there are rarely difficulties identifying many alternative models. Unfortunately, the constraints under which most assessments are conducted force the analyst to restrict the set of alternative models substantially. The implication of ignoring some plausible models is, of course, that uncertainty is under-estimated (to an unknown extent). The inability to consider a wide range of models (including models that imply that the assessment data are not indicative of trends in abundance) would explain some of the many spectacular assessment failures.

The process of choosing prior distributions can be very time-consuming and frustrating. Scientists who are experts with the species concerned but who are unaware of Bayesian techniques (and hence do not have a full understanding of what is meant by a prior distribution) can provide "prior distributions" which are either inconsistent or far too precise (Walters and Ludwig, 1994). Although "expert" opinion is currently the dominant method for determining priors, and is the source of many problems, we believe that prior distributions will increasingly be determined by analysis of information from synthesis studies and hence depend less on "expert" opinion (see Section 4.3). The majority of the problems encountered during the development of Bayesian assessments have resulted from arguments about the choice of prior distributions. In particular, considerable difficulties have arisen when attempts have been made to select appropriate noninformative prior distributions. In contrast, the development of informative priors tends to be productive with most participants in the stock assessment groups concerned cooperating even in fairly confrontational assessment situations.

Punt and Hilborn (1997) recommend that whenever a Bayesian assessment is conducted, considerable care should be taken to document fully the basis for the various prior distributions. This documentation process must include specifying which models were considered for inclusion in the analysis and why some of these models were not included in the final analyses, even though they may be plausible. We have found that the process of constructing priors increases the participation in the assessment process of non-modellers (i.e. biologists, industry, and members of the conservation movement). This increases the confidence that decision makers place in the assessment results because all of the stakeholders can have input into the assessment.

It is extremely intensive computationally to apply Bayes
Theorem to complex models. It often takes days of computer time even on
reasonably powerful personal computers to conduct an analysis based on an
age-structured model. The algebraic demands of the methods (e.g. the need for a
full understanding of probability theory) have also discouraged application of
the method. However, in order to conduct defensible decision analyses for
assessments based on maximum likelihood estimation, it is usually necessary to
conduct a bootstrap analysis (e.g. Restrepo *et al*., 1992). Such an
analysis, although not usually as intensive computationally as applying Bayes
Theorem, can often take several hours on a personal computer. Furthermore, even
seemingly simple approaches such as bootstrapping are not without their
theoretical traps (e.g. Poole *et al*., 1999).

While no approach to stock assessment can guarantee the
"correct" answer, the Bayesian approach to fisheries stock assessment provides
the most theoretically defensible framework within which probabilistic questions
(e.g. is the stock increasing, what is the impact of a *TAC* of 10,000
tonnes) can be addressed. The ability to consider model uncertainty within a
single framework, although currently underused, is a major advantage of Bayesian
methods. Finally, the Bayesian approach to fisheries stock assessment provides a
formal framework for incorporating information from other species and
stocks.