INFERENCE FROM A DETERMINISTIC POPULATION-DYNAMICS MODEL FOR BOWHEAD WHALES

We consider the problem of inference about a quantity of interest give n different sources of information linked by a deterministic populatio n dynamics model. Our approach consists of translating all the availab le information into a joint premodel distribution on all the model inp uts and outputs and then restricting this to the submanifold defined b y the model to obtain the joint postmodel distribution. Marginalizing this yields inference, conditional on the model, about quantities of i nterest, which can be functions of model inputs, model outputs. or bot h. Samples from the postmodel distribution are obtained by importance sampling and Rubin's SIR algorithm. The framework includes as a specia l case the situation where the pre-model information about the outputs consists of measurements with error; this reduces to standard Bayesia n inference. The results are in the form of a sample from the postmode l distribution and so can be examined using the full range of explorat ory data analysis techniques. Methods for comparing competing populati on dynamics models are developed. based on a generalization of the Bay es factor idea. A keg. quantity used by the International Whaling Comm ission (IWC) in making decisions about bowhead whales, Balaena mystice tus, is the replacement yield, RY. Information about the species is of three main types: recent census information. historical catch records . and evidence about birth and death rates. These are combined using a special case of the Leslie matrix population dynamics model. Our meth od yields full inference about RY and also sheds light on other. somet imes controversial. questions of scientific interest. These ideas are also applicable to many simulation models in other areas of science an d policy making. Software to implement these methods is available from StatLib.