In Season Forecasting of Skeena River Sockeye Run Size Using Bayesian Probability Theory

This report examines the utility of using Bayesian probability theory to combine several inseason estimators of Canadian Area 4 Skeena River sockeye run-size into a single best estimate of total return. The inseason estimators were configured in two separate Bayes models, and included Canadian Area 3x cumulative catch per effort (CPE) and catch by statistical week, Area 4 cumulative CPE and catch by statistical week, and the Inshore Run (Area 4 catch plus escapement) by statistical week. Nonlinear regressions of Area 4 total return versus each of these predictors were evaluated in a hind cast retrospective analysis for the years 1984-1994. The Bayesian composite forecasts were always more accurate than the least accurate component forecast, and sometimes better than the most accurate component forecast. Confidence intervals, calculated directly from the Bayes posterior distribution, included the true run size for all but the very largest return years. Prior probabilities, expressed as prior five-year average returns, had a variable impact on the Bayes composite forecasts, with some years benefiting form the use of priors, and other years not benefiting from the use of priors. The Mean Absolute Percent Error (MAPE) criterion identified the Bayes model using uniform priors, Area 3 cumulative CPE, Area 4 cumulative CPE, and the cumulative Inshore run, as performing slightly better than any of the other models tested. Forecast performance, for all models tested, improved as the season progressed. The Bayesian approach of using all available data to create a composite run-size forecast appears preferable to single-forecast methodologies.