TY - JOUR

T1 - Using the EM algorithm to weight data sets of unknown precision when modeling fish stocks

AU - Cotter, AJR

AU - Buckland, Stephen Terrence

PY - 2004/7

Y1 - 2004/7

N2 - Stocks of commercial fish are often modelled using sampling data of various types, of unknown precision, and from various sources assumed independent. We want each set to contribute to estimates of the parameters in relation to its precision and goodness of fit with the model. Iterative re-weighting of the sets is proposed for linear models until the weight of each set is found to be proportional to (relative weighting) or equal to (absolute weighting) the set-specific residual invariances resulting from a generalised least squares fit. Formulae for the residual variances are put forward involving fractional allocation of degrees of freedom depending on the numbers of independent observations in each set, the numbers of sets contributing to the estimate of each parameter, and the number of weights estimated. To illustrate the procedure, numbers of the 1984 year-class of North Sea cod (a) landed commercially each year, and (b) caught per unit of trawling time by an annual groundfish survey are modelled as a function of age to estimate total mortality, Z, relative catching power of the two fishing methods, and relative precision of the two sets of observations as indices of stock abundance. It was found that the survey abundance indices displayed residual variance about 29 times higher than that of the annual landings. Crown Copyright (C) 2004 Published by Elsevier Inc. All rights reserved.

AB - Stocks of commercial fish are often modelled using sampling data of various types, of unknown precision, and from various sources assumed independent. We want each set to contribute to estimates of the parameters in relation to its precision and goodness of fit with the model. Iterative re-weighting of the sets is proposed for linear models until the weight of each set is found to be proportional to (relative weighting) or equal to (absolute weighting) the set-specific residual invariances resulting from a generalised least squares fit. Formulae for the residual variances are put forward involving fractional allocation of degrees of freedom depending on the numbers of independent observations in each set, the numbers of sets contributing to the estimate of each parameter, and the number of weights estimated. To illustrate the procedure, numbers of the 1984 year-class of North Sea cod (a) landed commercially each year, and (b) caught per unit of trawling time by an annual groundfish survey are modelled as a function of age to estimate total mortality, Z, relative catching power of the two fishing methods, and relative precision of the two sets of observations as indices of stock abundance. It was found that the survey abundance indices displayed residual variance about 29 times higher than that of the annual landings. Crown Copyright (C) 2004 Published by Elsevier Inc. All rights reserved.

KW - iteratively weighted least squares

KW - generalised least squares

KW - fish stock assessment models

KW - degrees of freedom

KW - MAXIMUM-LIKELIHOOD

UR - http://www.scopus.com/inward/record.url?scp=2542420230&partnerID=8YFLogxK

UR - http://www.sciencedirect.com/science?_ob=ArticleURL&_aset=B-WA-A-W-A-MsSAYVW-UUW-AUEEYBEVWW-AUEDVWUWWW-ZZDEZEAYB-A-U&_rdoc=1&_fmt=summary&_udi=B6VHX-4CCFCTG-1&_coverDate=07%2F31%2F2004&_cdi=6078&_orig=search&_st=13&_sort=d&view=c&_acct=C000050565&_version=1&_urlVersion=0&_userid=1026342&md5=4fc8290870fce871736e01078afb7401

U2 - 10.1016/j.mbs.2004.03.001

DO - 10.1016/j.mbs.2004.03.001

M3 - Article

SN - 0025-5564

VL - 190

SP - 1

EP - 7

JO - Mathematical Biosciences

JF - Mathematical Biosciences

IS - 1

ER -