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Data and Management Strategies for Recreational Fisheries with Annual Catch Limits (2021) / Chapter Skim
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Appendix D: Bayesian Methods
Pages 185-194

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From page 185...
... Bayesianmodel. model that Thecould example be usedfocuses onman by fishery the manageme of a single-species fishery located in a particular geographic region, but the approach can be extended agers to set season lengths and decide on season closure dates under an annual catch limit (ACL)
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From page 186...
... and Prob(λ) are combined, it turns it turns out out that the resulting prior probability distribution is a negative binomial distribution with that the resulting prior probability distribution is a negative binomial distribution with parameters α and ν,parameters α and denoted ν, denoted NegBin NegBin νprior(X prior (X | αprior, prior | αprior )
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From page 187...
... before the arrival of any new MRIP data from the upcoming fishing season. ESTIMATING ESTIMATING THE THE OPTIMAL OPTIMAL FISHING FISHING SEASONSEASON LENGTHLENGTH USING USING THE THE PRIORPRIOR DISTRIBUTION DISTRIBUTION ItIt isis assumed assumed that that thethe fishery fishery manager's manager's objective objective isis to to maximize maximize thethe fishing fishing season season length length (measured (measuredhere herein indays)
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From page 188...
... . The prior probability distribution can be used to determine the fishing season length that meets this objective.
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From page 189...
... PER DAY (X) , AND UPDATE THE FISHING SEASON LENGTH USING As BAYESIAN new data arrive UPDATING during theTO INCORPORATE fishing season, the prior NEW INFORMATION, probability distributionOBTAIN of catch THE per POSTERIOR day, NegBinprior PROBABILITY (X|αprior,νprior)
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From page 190...
... , isisisthen is ) ,then then is then then used used used used toused to toto to update pdate updateupdate the the theestimate the estimate estimate estimate update of ofofthe the the of theprobability the probability estimate probability probability distribution distribution distribution of the probability distribution ofofcumulative of cumulative cumulative of distribution cumulative fish fish fish of cumulative fish catch catch catch catch atatat fish the the the at end catch the end end at end of the ofofend the the of theoffishing the fishing fishing thefishing season, season, season, fishing season, XXX ,X t,t,tgiven given given t, given by bybyNegBin NegBin by NegBin NegBin season, t, (X Xpost post post (X (X givent t|(X post t|α |αby αtpost post| NegBin ,α,t·ν post ,t·ν t·ν post,post t·ν post)
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From page 191...
... can be combined with the prior probability disof catch per day, NegBinprior (X | αprior, νprior) , to derive the new, updated, posterior probability distribution tribution of catch per day, NegBinprior(X | αprior,νprior)
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From page 192...
... ,then is then used used to to The updated probability distribution of catch per day, NegBin post(X | αpost, νpost) , is then used to update the estimate of the probability distribution of cumulative fish catch at the end of the fishing season, update the estimate of the probability distribution of cumulative fish catch at the end of the fishing update the estimate of the probability distribution of cumulative fish catch at the end of the fishing season, Xt, given season,by XNegBin t, given by(X post t | αpostpost NegBin , t·ν(X | αwhere: t )
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From page 193...
... EXTENSIONS AND APPLICATIONS OF THE BASIC BAYESIAN MODEL Given the basic Bayesian model outlined above, several extensions and applications of the model can be used to address additional questions relevant to in-season management of fisheries under an ACL. For example, the Bayesian model can be used to: • Compare fishery management outcomes under a fixed season length ("predictability")
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From page 194...
... For example, when an underage increases the ACL in the subsequent year or an overage decreases the ACL in the subsequent year, the model can be used to estimate the effects on the probability distribution of season length in the subsequent year. • Assess via simulation whether particular ancillary variables (e.g., weather, water tempera ture, fuel prices, unemployment rate)
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Key Terms

  • season length
  • probability distribution
  • prior prior
  • negative binomial
  • fishery managers

  • prior probability
  • fish catch
  • remaining fishing
  • total catch
  • gamma distribution

  • data arrive
  • mrip data
  • bayesian updating
  • previous fishing
  • cumulative fish

  • binomial distribution
  • annual catch
  • bayesian model
  • solver feature
  • fishing effort

  • maximum season
  • binomial probability
  • updated probability
  • total fish
  • data quality

  • mean catch
  • catch limits
  • whereby prob
  • days days
  • fishing day


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