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Fishery Bulletin 96(3), 1 998 
C(w) - estimator as a function of uncorrected 
data 
C(w F p C ) = estimator as a function of data cor- 
rected with an estimated FPC, 
where w = (x v x 2 , . . . , , y v y 2 , . . . y n ) 
= a mixed vector of CPUE observations 
from two vessels 
and 
w F pc = {x v x 2 , . . . , x n ,y 1 FPC,y t) FPC, . . . 
y n JPO 
- a mixed vector of CPUE observations 
and estimates, 
a model for the decision rule can be stated as: Apply 
the FPC if 
MSE 
C(w) 
> MSE 
C{w 
— FPC ' 
ference for which correcting reduces the MSE of the 
estimated mean CPUE can then be determined. 
This general strategy is illustrated by construct- 
ing an algorithm to apply it to a real problem. Any 
algorithm for implementing this decision rule will 
depend on specific circumstances. In this case the 
particulars are defined by a fishing power problem 
in an annual survey of the eastern Bering Sea, con- 
ducted by the AFSC (Wakabayashi et al., 1985; 
Goddard and Zimmermann 1 ). Two vessels system- 
atically sample all strata, following interleaved sta- 
tion patterns that produce approximately equal num- 
bers of CPUE observations. From these two sets of 
unpaired data a fishing power difference between two 
vessels is estimated for each of a number of species. 
The question is “Should this estimated FPC be used 
to correct CPUEs of one vessel to the fishing effi- 
ciency of the other?” This general MSE decision rule 
takes the following form (the specifics of the Bering 
Sea survey being addressed within this framework): 
and do not apply the FPC if 
MSE\C{w) 
< MSE 
C (iv ppp ) 
(Note, this explication of the MSE of mean CPUE 
has been framed in terms of a single survey with 
two vessels. But the notion of MSE lends itself 
equally well to any situation in which data must be 
“corrected,” including the common case of a single, 
nonstandard vessel conducting a standard survey.) 
This decision rule is unattainable because it re- 
quires that the true value of the fishing power dif- 
ference and CPUE sampling distributions be known. 
However, simulations can be used to estimate the 
mean square error. One such simulation strategy 
takes the following form: Assume a probability dis- 
tribution for CPUE. Generate realizations of this dis- 
tribution to represent a survey in which a fishing 
power difference is suspected. Impose an assumed 
fishing power difference on the simulated survey. 
Estimate the fishing power difference and apply the 
estimate to correct the assumed fishing power dif- 
ference. ( Estimating the fishing power difference may 
require further distributional assumptions and simu- 
lations, depending on the estimator and the kind of 
data it requires, especially if fishing power differ- 
ence is to be estimated from experiments conducted 
independently of the survey.) The MSEs of the esti- 
mated mean CPUE are then calculated from the re- 
alizations with and with out the fishing power cor- 
rections. This procedure is repeated for a range of 
selected fishing power differences. Whether the ob- 
served fishing power difference (estimated from real 
data) falls within the range of the fishing power dif- 
1 Simulate surveys from an appropriate sampling 
distribution for data collected by a “standard” 
vessel. 
2 Impose a known fishing power difference on the 
CPUE data in each simulated survey. (In these 
examples half the data were altered to emulate a 
two-vessel survey.) 
3 For each simulated survey, estimate an FPC to 
correct the fishing power difference that was im- 
posed in the previous step. (FPCs may be esti- 
mated from simulation from independent experi- 
mental data or, as in these examples, estimated 
from the simulated survey itself. The important 
aspect is that the error structure of the FPC esti- 
mator be incorporated in the simulation process.) 
4 Estimate the mean CPUE for each simulated sur- 
vey with and without correcting for the fishing 
power difference. 
5 Repeat steps 2 through 4 for a range of fishing 
power differences. 
6 Compute MSEs for estimated mean CPUE for 
each level of fishing power difference. 
7 Plot the estimated MSEs against the fishing 
power differences imposed in Step 2 (Fig. 1). 
8 Determine the range of fishing power difference 
where the MSE for corrected data is lower than 
the MSE for uncorrected data (Fig. 1). 
The region of increased error is centered around the 
value 1.0, which represents equal fishing powers, and is 
sandwiched between regions of reduced error (Fig. 1). 
The smaller the true fishing power difference the 
more likely that correcting it will lead to increased 
error in mean CPUE, and the greater the fishing 
