Abundance Estimation from Multiple Photo Surveys: Confidence Distributions and Reduced Likelihoods for Bowhead Whales off Alaska

Maximum likelihood estimates of abundance are obtained from repeated photographic surveys of a closed stratified population with naturally marked and unmarked individuals. Capture intensities are assumed log-linear in stratum, year, and season. In the chosen model, an approximate confidence distribution for total abundance of bowhead whales, with an accompanying likelihood reduced of nuisance parameters, is found from a parametric bootstrap experiment. The confidence distribution depends on the assumed study protocol. A confidence distribution that is exact (except for the effect of discreteness) is found by conditioning in the unstratified case without unmarked individuals.