Bayesian Time-Stratified-Petersen Estimators for Abundance

Simple-Petersen or Stratified-Petersen methods are often used to estimate number of outgoing smolt or returning salmon. These methods are inadequate to deal with heterogeneity in catchability among strata and with missing data from strata caused by crew illness, high water flow, or other causes. We propose a Bayesian spline-based methodology to estimate abundance and run-timing which provides several compelling advantages over the more traditional estimators. The hierarchical model for capture probabilities and the spline model for the general shape of the run curve, allow information to be shared among strata within a Bayesian framework and allows great flexibility to deal with missing data. It is self-calibrating. For strata with poor data, extensive pooling across strata take place but with strata with rich data, the information for a particular stratum takes precedence. The methodology automatically adjust measures of precision for heterogeneity in catchability among strata (which is ignored in the simple-Petersen) and shares information from neighbouring strata (unlike the Stratified-Petersen). Examples from estimating the number of outgoing number of salmon smolt in the Trinity River, CA will be presented.