Layman's abstract:Hierarchical Bayesian small area estimation for circular data


  • Author: Daniel Hernandez-Stumpfhauser, F. Jay Breidt, Jean D. Opsomer
  • Date: 28 July 2017
  • Copyright: © Statistical Society of Canada

As a new initiative on Statistics Views we will be publishing layman's abstracts of articles to coincide with their publication on Wiley Online Library. The aim is to highlight research to a broader audience. This article featured in the series is from The Canadian Journal of Statistics: Hierarchical Bayesian small area estimation for circular data by Daniel Hernandez-Stumpfhauser, F. Jay Breidt, Jean D. Opsomer.

Read the layman's abstract below.

Daniel Hernandez-Stumpfhauser, F. Jay Breidt, Jean D. Opsomer. (2016), Hierarchical Bayesian small area estimation for circular data, The Canadian Journal of Statistics, 44, pages 416–430, doi: 10.1002/cjs.11303

thumbnail image: Layman's abstract:Hierarchical Bayesian small area estimation for circular data

In the United States, the National Marine Fisheries Service monitors recreational fishing in salt water along the Atlantic and Gulf Coast. Estimates of recreational fishing catch, which are essential for assessing the health of the fishery and for its regulation, are obtained by estimating the catch per angler trip and multiplying by an estimate of the number of angler trips. The catch per trip is estimated from on-site “intercept” surveys, in which interviews are conducted with anglers as they depart from fishing access sites along the coasts. The number of angler trips is separately estimated using data from a telephone survey.

Part of the weighting procedure for the data from the intercept survey involves extrapolating from the observed angler departures, during the time the interviewer spent on-site, to angler departures throughout the day, including those times when the interviewer was not present. Extensive data on these departure times are available from the telephone survey, but estimates are needed for over 400 domains formed by crossing 17 states, six two-month temporal “waves”, and four different modes of fishing. Over 10% of these domains have no observations, while many others have sample sizes too small for reliable direct estimation of the departure time distributions.

Researchers from the United States have addressed this estimation challenge by developing a novel small area estimation technique for distributions on the circle; in this case, the 24-hour clock. The method is based on the projected normal distribution, which models an observation on the circle as a realization of a bivariate normal random vector that has been normalized to unit length. Regression models for the mean structure of the bivariate normal distribution allow the method to “borrow strength” across domains. A hierarchical Bayesian approach to inference is adopted via a Hamiltonian Monte Carlo scheme due to the non-standard distributions in the prior and the relatively large number of parameters. The resulting methodology produces valid estimated distribution functions on the 24-hour clock for every required domain, converging to the direct data-based estimate when observations are plenty and reducing variation by shrinking toward a unimodal circular projected normal distribution when observations are sparse.

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