PARRACK: FISHING EFFORT FROM AERIAL SEARCH DATA 



which reduces to 



PiG) =9^n; 



so that the equation may be solved for days on 

 grounds: 



9 = nP{G). 



Then by substitution 



g = n[(g' ^ n) + P(G/N)in - g') ^ n],or 

 g^g' + P{G/N){n-g'). 



Estimator II is then derived by inclusion of the 

 ratio of days fished to days on grounds, K = f -^ g, 

 so that the above algorithm may be expressed in 

 terms of days fished: 



f=K{g' + PiG/N)in-g')]. 



An estimate of days fished (./) may be made, then, 

 from surveillance overflight data if calculations of 

 R and P{G/N) can be made from past data. 



Estimator III is deduced from the event space 

 according to the same rationale. The likelihood of 

 an event of a vessel day fished expressed as 

 observed and not observed is expanded to calculate 

 days fished. From the event space it is apparent 

 that: 



P{F) = P{F, N) + P{F, S) 



where PiF) is the probability of a vessel day fished, 

 P{F, N) is the probability of a vessel day fished and 

 not observed on overflights, and P{F, S) is the 

 probability of a vessel day fished and observed on 

 overflights. Further, by application of the multi- 

 plication theorem of probabilities 



P{F,K} = P{F/N)-P{N) 



where P{F/N) is the probability of a vessel day 

 fished given that it was not observed on over- 

 flights, and P{N) is the probability that a possible 

 vessel day (regardless of location or operational 

 mode) was not observed on overflights. The first 

 expression therefore can be written as 



P{F) = P(F/N)P{N) + P{F,S). 



Although all possible probabilities can be ex- 

 pressed in terms of the number of events in each 

 category of the event space, those of interest are: 



P(F,S)=f'/n, 



P{N) =(« -.g')/«, and 

 P{F/N)={f-f)/in-g'). 



By substitution and reduction of terms 



PiF) =f/n. 



The number of vessel days fished, then, is the 

 product of the entire event space and the 

 probability of fishing, i.e., 



/= nPiF). 



Then, by substitution, estimator III easily follows 

 so that days fished are estimable from overflight 

 data if PiF/N) can be predetermined from past 

 data: 



f = f' + PiF/N)in-g'). 



From possible algorithms derivable from the 

 event space, this form makes most use of over- 

 flight data and is least dependent on functions 

 calculated from past data. 



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