Ben O'Neill

Importance sampling for Bayesian sensitivity analysis

We examine the use of sensitivity analysis with a particular focus on calculating the bounds of imprecise previsions in Bayesian statistics. We explain the use of importance sampling in approximating the range of these imprecise previsions and we develop an approximation function for the imprecise posterior prevision based on generating a finite number of random variables. We develop a convergence theorem that shows that this approximation converges almost surely to the posterior prevision as we generate more and more random variables. We also develop a useful accuracy bound for the approximation for a large finite number of generated random variables. We test the efficiency of this approximation using a simple example involving the imprecise Dirichlet model.

Some Useful Moment Results in Sampling Problems

We consider the standard sampling problem involving a finite population of N objects and a sample of n objects taken from this population using simple random sampling without replacement. We consider the relationship between the moments of the sampled and unsampled parts and show how these are related to the population moments. We derive expectation, variance, and covariance results for the various quantities under consideration and use these to obtain standard sampling results with an extension to variance estimation with a “finite population correction.” This clarifies and extends standard results in sampling theory for the estimation of the mean and variance of a population.

Evidence of separate subgroups of juvenile southern bluefin tuna

Abstract Archival tagging studies of southern bluefin tuna (SBT , Thunnus maccoyii) have revealed that juveniles residing in the Great Australian Bight (GAB) over the austral summer undertake seasonal cyclic migrations to the southeast Indian Ocean and the Tasman Sea during winter. However, there remains disagreement about the extent of mixing between juvenile SBT regularly caught by longline fleets south of Africa and those observed in the GAB. Some researchers have argued that archival tag recoveries indicate most juveniles reside in the GAB over the austral summer. Others have suggested that recoveries of conventional and archival tags are better explained by a juvenile population consisting of separate groups on the eastern and western sides of the Indian Ocean with limited intermixing. We present analyses of catch and tag recovery data and re‐examine archival tagging studies. The evidence provided strongly favors the hypothesis of separate juvenile subgroups, or contingents, with limited intermixing. We draw some tentative conclusions about the nature of the putative contingents and discuss some implications of these findings for the interpretation of existing datasets and future research priorities. We also provide the first evidence that the migration choices of juveniles that summer in the GAB are influenced by fidelity to winter feeding grounds and suggest this helps explain the collapse of the surface fishery off New South Wales in the 1980s.