Samu Mäntyniemi FEM, U. Helsinki, Sakari Kuikka FEM, U. Helsinki

1. Evaluation of standard ICES stock assessment and Bayesian stock assessment in the light of uncertainty: North Sea herring as an example Samu Mäntyniemi FEM, U. Helsinki, Sakari Kuikka FEM, U. Helsinki Richard Hillary Imp. College Henrik Sparholt ICES ICES Annual Science Conference 2007, Helsinki

2. Uncertainty • Does uncertainty exist? • How is it currently taken into account in ICES stock assessment? • Science behind the methods • Do they match the questions? • How about the Bayesian approach?

3. Uncertainty: does it exist? • Uncertainty : lack of knowledge • Knowledge • Exist in the context of a person • Uncertainty does not exist as an objective, physical quantity • Next question: WHOSE uncertainty should be measured?

4. Whose uncertainty is relevant? • The only uncertainty that affects management decisions is the one possessed by the managers • Managers may ask for advice and adopt the uncertainty of an expert group • Importance of communication! ICES Manager: Decision ACFM: Review Advice Stock assessment WG: Expertise

5. What should we do in stock assessment WG? • What do we know about the stock based on.. • Basic biological knowledge • Repeated spawning? Fecundity? Schooling behav.? • Experience from other stocks • Stock-recruitment parameters of a similar stock • Interpretation of data sets • Population dynamics & knowledge of the sampling process • Quantitative assessement: • Report quantitative measures of our uncertainty about the status of the stock.

6. “Standard” ICES stock assessment • Herring Assessment Working Group for the Area South of 62° N (HAWG) was taken to represent the mainstream of stock assessment methods used in ICES • Methods used by HAWG • Point estimates (Maximum Likelihood) & variances • Confidence intervals • Bootstrap distributions • Monte Carlo forward projection with STPR3

7. N p(C|N) Chyp p(N|C=5) N p(NhypML|NML) ICES method : “frequentist statistics” Fr. probability of catch if N was known? Hypothetical repeated catches? Chyp? N? C=5 Analytics Bootstrap Delta-meth. Monte Carlo

8. ICES methods: summary • Measure of uncertainty: frequency probability • Relies on concept of repeatable experiment, describes sampling variation • Can not be assigned to unknown states of nature • probability statements about stock size are conceptually impossible! • Focus on behavior of point estimates

9. Existing knowledge p(N|C=5) N Alternative : Bayesian statistics Probability of data p(C|N) p(N) N? N C C=5 Analytics MCMC SIR PMC

10. Bayesian approach: summary • Interpretation of probability: personal degree of belief • Measure of one’s uncertainty • Probability statements about the state of nature • Integration of existing knowledge and interpretation of data in a consistent way • No ad hoc comparison of “results” and background knowledge necessary for final conclusions • Focus of inference • Uncertainty about all unknown quantities given the observed data

11. Conclusions I • Standard ICES stock assessment methods do not directly measure the uncertainty of the assessment group about the fish stock • If so, why are these methods used? • For decades the Bayesian approach was not computationally feasible • Fr. approach was the only option to estimate something

12. Conclusions II • If ICES would adopt the Bayesian approach… • Scientifically more sound: unified theory of making inference • More transparent: roles and weights of different sources of information are made explicit in the mathematical model • Decision analysis • Improves possibility to account for stakeholder values • Needs clear definition of management objectives

13. Bayesian approach already in use • ICES WGBAST: since 2002 • Presentation O:31 at 14:30 • USA: Pacific Salmon Commission • Models under development for ICES stocks in EU projects: • PRONE: NS herring • POORFISH: Baltic herring

14. NS herring: example Thank You!