A generalized predictive probability density for in-season forecast of anadromous fish return abundance

For conservation of anadromous fish, managers rely on in-season forecast of return more than on preseason forecast whose accuracy and precision are questionable because preseason forecast is made several months prior to fish’ arrival at the river mouth.  The objective is to develop a generalized probability density function (pdf) for in-season forecast of anadromous fish return, which can be used regardless of species and setting.  Data for in-season forecast are from monitor of daily return number and thus in-season forecast is made on a daily basis during a return season.  Most previous studies failed to capture year-to-year variability in return timing, and provided only point value of unknown return.  Although Fried and Hilborn (1988) and Hyun et al. (2005) expressed the variance of forecast with gamma and lognormal pdfs, these pdfs are not robust.  Another objective is to evaluate uncertainty in parameters that govern the general predictive pdf.  Some referees often overstate Bayesian method by arguing that it takes account of uncertainty in estimates of parameters and predicted value of a unknown random variable whereas maximum likelihood method does not.  I challenge and discuss the overstatement.  For demonstration, I used actual data on sockeye salmon return to Alaska Bristol Bay.