INFERENCE ABOUT THE RATIO OF 2 PARAMETERS, WITH APPLICATION TO WHALE CENSUSING

Inference for the quotient of two parameters estimated separately may be obtained by the delta method. When the distribution of linear trans formations involving the numerator and the denominator is available, m ore exact and elementary methods may be used. Non-Bayesian and Bayesia n approaches are developed. The application of the methods to estimati ng the stock abundance of Northeastern Atlantic minke whales, where th e ratio is a raw estimate divided by a measure of observation efficien cy, is explained and discussed. The Bayesian approach allows exact inf erence in quite general situations using only a single, rapidly implem ented, one-dimensional numerical integration. A simple analytic approx imation is given for the common situation where the joint posterior di stribution of the numerator and denominator can be approximated by a n ormal distribution that gives very little probability to negative valu es of the denominator. The Bayesian approach also permits the incorpor ation of model uncertainty (or disagreement) in a natural way, and thi s was the basis for the conclusions of the International Whaling Commi ssion Scientific Committee at its 1990 meeting.