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Variational Approximations for Selecting Hierarchical Models of Circular Data in a Small Area Estimation Application

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  • Hernandez-Stumpfhauser Daniel

    (University of North Carolina–Chapel Hill, ; Colorado, ; United States)

  • Breidt F. Jay

    (Colorado State University, ; Colorado, ; United States)

  • Opsomer Jean D.

    (Colorado State University, ; Colorado, ; United States)

Abstract

We consider hierarchical regression models for circular data using the projected normal distribution, applied in the development of weights for the Access Point Angler Intercept Survey, a recreational angling survey conducted by the US National Marine Fisheries Service. Weighted estimates of recreational fish catch are used in stock assessments and fisheries regulation. The construction of the survey weights requires the distribution of daily departure times of anglers from fishing sites, within spatio-temporal domains subdivided by the mode of fishing. Because many of these domains have small sample sizes, small area estimation methods are developed. Bayesian inference for the circular distributions on the 24-hour clock is conducted, based on a large set of observed daily departure times from another National Marine Fisheries Service study, the Coastal Household Telephone Survey. A novel variational/Laplace approximation to the posterior distribution allows fast comparison of a large number of models in this context, by dramatically speeding up computations relative to the fast Markov Chain Monte Carlo method while giving virtually identical results.

Suggested Citation

  • Hernandez-Stumpfhauser Daniel & Breidt F. Jay & Opsomer Jean D., 2016. "Variational Approximations for Selecting Hierarchical Models of Circular Data in a Small Area Estimation Application," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 91-104, March.
    • Handle: RePEc:vrs:stintr:v:17:y:2016:i:1:p:91-104:n:8
    DOI: 10.21307/stattrans-2016-007
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    References listed on IDEAS

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    1. Ormerod, J. T. & Wand, M. P., 2010. "Explaining Variational Approximations," The American Statistician, American Statistical Association, vol. 64(2), pages 140-153.
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