A hierarchical Bayesian model for estimating historical salmon escapement and escapement timing

In this paper, we present an improved methodology for estimating salmon escapements from stream count data. The new method uses a hierarchical Bayesian model that improves estimates in years when data are sparse by "borrowing strength" from counts in other years. We present a model of escapement and of count data, a hierarchical Bayesian statistical framework, a Gibbs sampling approach for evaluation of the posterior distributions of the quantities of interest, and criteria for determining when the model and inference are adequate. We then apply the hierarchical Bayesian model to estimating historical escapement and escapement timing for pink salmon (Oncorhynchus gorbuscha ) returns to Kadashan Creek in Southeast Alaska. Resume : On trouvera ici une methodologie amelioree pour estimer les echappees de saumon a partir des donnees de denombrement dans un cours d'eau. La nouvelle methode utilise un modele hierarchique bayesien (HBM) qui ameliore les estimations pour les annees ou les donnees sont rares en " empruntant de la puissance " aux denombrements des autres annees. Nous presentons un modele pour les donnees d'echappees et de denombrement, un cadre statistique hierarchique bayesien, une strategie d'echantillonnage de type Gibbs pour l'evaluation des distributions a posteriori des valeurs recherchees et des criteres pour determiner quand le modele et les inferences sont adequats. Nous appliquons le modele HBM a l'estimation des echappees des annees anterieures et du moment des retours des Saumons roses a Kadashan Creek dans le sud-est de l'Alaska. (Traduit par la Redaction) Su et al. 1662

[1]  ESTIMATION OF SALMON ESCAPEMENT: MODELS WITH ENTRY, MORTALITY AND STOCHASTICITY , 1997 .

[2]  M. Fukushima,et al.  Determinants of stream life, spawning efficiency, and spawning habitat in pink salmon in the Auke Lake system, Alaska , 1997 .

[3]  J. Q. Smith,et al.  1. Bayesian Statistics 4 , 1993 .

[4]  A. Raftery,et al.  How Many Iterations in the Gibbs Sampler , 1991 .

[5]  Thomas P. Quinn,et al.  Pacific Salmon Life Histories , 1992 .

[6]  W. J. Langford.  Statistical Methods , 1959, Nature.

[7]  Zhenming Su,et al.  A comparison of salmon escapement estimates using a hierarchical Bayesian approach versus separate maximum likelihood estimation of each year's return , 2001 .

[8]  Terrance J. Quinn,et al.  Quantitative Fish Dynamics , 1999 .

[9]  Zhenming Su,et al.  Optimal in-season management of pink salmon (Oncorhynchus gorbuscha) given uncertain run sizes and seasonal changes in economic value , 2002 .

[10]  A. Rukhin.  Bayes and Empirical Bayes Methods for Data Analysis , 1997 .

[11]  Philip Heidelberger,et al.  Simulation Run Length Control in the Presence of an Initial Transient , 1983, Oper. Res..

[12]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[13]  Benjamin W. Van Alen,et al.  Observer Accuracy and Precision in Aerial and Foot Survey Counts of Pink Salmon in a Southeast Alaska Stream , 1998 .

[14]  Ray Hilborn,et al.  Estimating spawning escapements from periodic counts : a comparison of methods , 1999 .

[15]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[17]  Frederick Mosteller,et al.  Some Progress and Problems in Meta-Analysis of Clinical Trials , 1992 .

[18]  Russell B. Millar,et al.  Bayesian state-space modeling of age-structured data: fitting a model is just the beginning , 2000 .

[19]  G. Casella,et al.  The Effect of Improper Priors on Gibbs Sampling in Hierarchical Linear Mixed Models , 1996 .

[20]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[21]  O. A. Mathisen,et al.  Life history of pink salmon (Oncorhynchus gorbuscha) and implications for management , 1983 .

[22]  Alan E. Gelfand,et al.  Model Determination using sampling-based methods , 1996 .

[23]  D. Lindley,et al.  Bayes Estimates for the Linear Model , 1972 .

[24]  R. Hilborn,et al.  Reconstruction of Harvest Rates and Stock Contribution in Gauntlet Salmon Fisheries: Application to British Columbia and Washington Sockeye (Oncorhynchus nerka) , 1988 .

[25]  Effects of observer efficiency, arrival timing, and survey life on estimates of escapement for steelhead trout (Oncorhynchus mykiss) derived from repeat mark-recapture experiments , 2002 .

[26]  Marie Davidian,et al.  Nonlinear Models for Repeated Measurement Data , 1995 .

[27]  Robin J Wyatt,et al.  Estimating riverine fish population size from single- and multiple-pass removal sampling using a hierarchical model , 2002 .

[28]  E. Rivot,et al.  Hierarchical Bayesian analysis of capture-mark-recapture data , 2002 .

[29]  J. Irvine,et al.  A robust procedure for estimating salmon escapement based on the area-under-the-curve method , 1992 .

[30]  Ray Hilborn,et al.  Depensation in fish stocks : a hierarchic Bayesian meta-analysis , 1997 .

[31]  John Geweke,et al.  Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments , 1991 .

[32]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[33]  Walter R. Gilks,et al.  BUGS - Bayesian inference Using Gibbs Sampling Version 0.50 , 1995 .