2016 | 17 | 1 | 91-104
Article title

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

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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.
Physical description
  • University of North Carolina–Chapel Hill
  • Colorado State University
  • Colorado State University
  • BISHOP, C. M., (2006). Pattern Recognition and Machine Learning. Springer.
  • FAY, R. E., HERRIOT, R. A., (1979). Estimation of Income from Small Places: An Application of James-Stein Procedures to Census Data. Journal of the American Statistical Association 74, 269–277.
  • GELMAN, A., CARLIN, J. B., STERN, H. S., RUBIN, D. B., (2004). Bayesian Data Analysis. Chapman & Hall/CRC.
  • HERNANDEZ-STUMPFHAUSER, D., (2012). Topics in Design-Based and Bayesian Inference for Surveys. Ph. D. thesis, Colorado State University.
  • NEAL, R. M., (2003). Slice Sampling. The Annals of Statistics 31, 705–741.
  • NUÑEZ-ANTONIO, G., GUTIÉRREZ-PEÑA, E., (2005). A Bayesian Analysis of Directional Data Using the Projected Normal Distribution. Journal of Applied Statistics 32(10), 995–1001.
  • NUÑEZ-ANTONIO, G., GUTIÉRREZ-PEÑA, ESCALERA, E. G., (2011). A Bayesian Regression Model for Circular Data Based on the Projected Normal Distribution. Statistical Modeling 11, 185–201.
  • ORMEROD, J. T., WAND, M. P., (2010). Explaining Variational Approximations. The American Statistician 64, 140–153.
  • PRESNELL, B., MORRISON, S. P., LITTELL, R. C., (1998). Projected Multivariate Linear Models for Directional Data. Journal of the American Statistical Association 93(443), 1068–1077.
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