144 



Abstract.— Monte Carlo simulation 

 from probability distributions is often 

 favored as a means of quantifying the 

 uncertainty in the results of a popula- 

 tion analysis. Observed data are com- 

 bined with simulations from a popula- 

 tion model by using subjective distri- 

 butions for model parameters for which 

 no data are available. The results from 

 such methods can unfortunately be in- 

 accurate unless care is taken in the 

 combination of these simulations and 

 the observed data. A Monte Carlo 

 method was proposed at the 1996 meet- 

 ing of the Scientific Committee of the 

 International Whaling Commission for 

 the assessment of the Bering-Chukchi- 

 Beaufort Seas stock of bowhead whales. 

 We show that this method is potentially 

 inaccurate, and as such, it appears to 

 be unsuited to the bowhead application 

 and thus possibly to other similarly 

 structured management problems. 



A proposed stock assessment method and 

 its application to bowhead whales, 

 Balaena mysticetus 



David Poole 



Department of Statistics 

 P.O. Box 354322 

 University of Washington 

 Seattle, Washington 98195-4322 

 E-mail address poole g'stat wasfiington edu 



Geof H. Givens 



Department of Statistics 

 Colorado State University 

 Fort Collins, Colorado 80523 



Adrian E. Raftery 



Department of Statistics 

 University of Washington 

 PO Box 354322 

 Seattle, Washington 98195-4322 



Manuscript accepted 18 March 1998. 

 Fish. Bull. 97:144-152 ( 1999). 



The variability in parameter esti- 

 mates from a population analysis is 

 of great interest to stock assessment 

 scientists. Monte Carlo simulation 

 is an intuitively appealing and eas- 

 ily applied strategy for quantifying 

 this uncertainty. Over the past six 

 years, various Monte Carlo assess- 

 ment methods for the Bering- 

 Chukchi-Beaufort stock of bowhead 

 whales, Balaena niysticetus, have 

 been discussed by the Scientific 

 Committee of the International 

 Whaling Commission (IWC). A 

 Bayesian approach (Raftery et al., 

 1995) was adopted and used as the 

 basis for the IWC assessment of the 

 stock in 1994. The method was de- 

 veloped after a 1991 Scientific Com- 

 mittee (SO recommendation that 

 methods for taking full account of 

 uncertainty about inputs and out- 

 puts to population dynamics mod- 

 els be developed. An alternative 

 maximum likelihood approach was 

 also used for bowheads (Butter- 

 worth and Punt, 1995; Punt and 

 Butterworth, 1996). In contrast to 

 the adopted method, the latter ap- 



proach does not allow for uncer- 

 tainty in the values of various bio- 

 logical parameters. Rather, it as- 

 sumes that they are known exactly. 



At the 1996 SC meeting, a modi- 

 fied maximum likelihood assess- 

 ment to account for uncertainty in 

 biological parameters was consid- 

 ered (Punt and Butterworth, 1997). 

 The assessment method was an ap- 

 plication of a Monte Carlo approach 

 developed by Restrepo et al. ( 1991, 

 1992 ). Punt and Butterworth ( 1997) 

 cited an example of the use of the 

 Monte Carlo approach by the Inter- 

 national Commission for the Con- 

 servation of Atlantic Tunas, and 

 Restrepo et al. (1992) applied their 

 approach to swordfish and cod fish- 

 ery assessments. 



In our paper, we review the pro- 

 posed Monte Carlo approach, both 

 in general and in the specific bow- 

 head application, and evaluate its 

 performance and its compliance 

 with established statistical prin- 

 ciples. We show that in some cir- 

 cumstances the method can provide 

 suboptimal results for bowhead as- 



