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Original Articles

Bayesian analysis of circular distributions based on non-negative trigonometric sums

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Pages 3175-3187 | Received 02 Apr 2015, Accepted 09 Feb 2016, Published online: 25 Feb 2016

References

  • Batschelet E. Circular statistics in biology. London: Academic Press; 1981.
  • Fisher NI. Statistical analysis of circular data. Cambridge: Cambridge University Press; 1993.
  • Jammalamadaka SR, SenGupta A. Topics in circular statistics. Singapore: World Scientific Publishing, Co; 2001.
  • Upton GJG, Fingleton B. Spatial data analysis by example, Vol. 2 (Categorical and directional data). Chichester: John Wiley and Sons; 1989.
  • Fejér L. Über trigonometrische polynome. J Reine Angew Math. 1915;146:53–82.
  • Fernández-Durán JJ. Circular distributions based on nonnegative trigonometric sums. Biometrics. 2004;60:499–503. doi: 10.1111/j.0006-341X.2004.00195.x
  • Fernández-Durán JJ. Models for circular-linear and circular-circular data constructed from circular distributions based on nonnegative trigonometric sums. Biometrics. 2007;63:579–585. doi: 10.1111/j.1541-0420.2006.00716.x
  • Fernández-Durán JJ, Gregorio-Domínguez MM. Maximum likelihood estimation of nonnegative trigonometric sum models using a Newton-like algorithm on manifolds. Electron J Stat. 2010;4:1402–1410. doi: 10.1214/10-EJS587
  • Fernández-Durán JJ, Gregorio-Domínguez MM. CircNNTSR: an R package for the statistical analysis of circular data using nonnegative trigonometric sums (NNTS) models. 2013. Available from: http://CRAN.R-project.org/package=CircNNTSR R package version 2.1.
  • Bai ZD, CR Rao, Zhao LC. Kernel estimators of density function of directional data. J Multivariate Anal. 1988;27:24–39. doi: 10.1016/0047-259X(88)90113-3
  • Hall P, Watson GS, Cabrera J. Kernel density estimation with spherical data. Biometrika. 1987;74:751–762. doi: 10.1093/biomet/74.4.751
  • McVinish R, Mengersen K. Semiparametric Bayesian circular statistics. Comput Statist Data Anal. 2008;52:4722–4730. doi: 10.1016/j.csda.2008.03.016
  • Taylor CC. Automatic bandwidth selection for circular density estimation. Comput Statist Data Anal. 2008;52:3493–3500. doi: 10.1016/j.csda.2007.11.003
  • Nuñez-Antonio G, Gutiérrez-Peña E. A Bayesian analysis of directional data using the projected normal distribution. J Appl Stat. 2005;32:995–1001. doi: 10.1080/02664760500164886
  • Ravindran P. Bayesian analysis of circular data using wrapped distributions [Ph.D. thesis]. Raleigh (NC): North Carolina State University; 2002.
  • Ravindran P, Ghosh SK. Bayesian analysis of circular data using wrapped distributions. J Statt Theory Pract. 2011;5:547–561. doi: 10.1080/15598608.2011.10483731
  • Wang F, Gelfand AE. Directional data analysis under the general projected normal distribution. Stat Methodol. 2013;10:113–127. doi: 10.1016/j.stamet.2012.07.005
  • Gilks WR, Richardson S, Spiegelhalter D, editors. Markov Chain Monte Carlo in practice. New York: Chapman and Hall/CRC; 1995.
  • Courant R, John F. Introduction to calculus and analysis. New York: John Wiley and Sons; 1974.
  • Fan Y, Sisson SA. Reversible jump MCMC. In: Brooks S, Gelman A, Jones GL, Meng X-L, editors. Handbook of Markov Chain Monte Carlo. Boca Raton (FL): Chapman and Hall/CRC; 2011. p. 67–92.
  • Green PJ. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika. 1995;82:711–732. doi: 10.1093/biomet/82.4.711
  • Hastie DI, Green PJ. Model choice using reversible jump Markov chain Monte Carlo. Statist Neerlandica. 2012;66:309–338. doi: 10.1111/j.1467-9574.2012.00516.x
  • Sisson SA. Transdimensional Markov chains: a decade of progress and future perspectives. J Amer Statist Assoc. 2005;100:1077–1089. doi: 10.1198/016214505000000664
  • Hastings WK. Monte Carlo sampling methods using Markov chains and their applications. Biometrika. 1970;57:97–109. doi: 10.1093/biomet/57.1.97
  • Byrne S, Girolami M. Geodesic Monte Carlo on embedded manifolds. Scand J Statist. 2013;40:825–845. doi: 10.1111/sjos.12036
  • Roberts GO, Gelman A, Gilks WR. Weak convergence and optimal scaling of random walk Metropolis algorithms. Ann Appl Probab. 1997;7:110–120. doi: 10.1214/aoap/1034625254
  • Flegal JM, Haran M, Jones GL. Markov chain Monte Carlo: Can we trust the third significant figure? Statist Sci. 2008;23:250–260. doi: 10.1214/08-STS257
  • Marrero O. The performance of several statistical tests for seasonality in monthly data. J Stat Comput Simul. 1983;17:275–296. doi: 10.1080/00949658308810666
  • Stephens MA. Techniques for directional data. Stanford (CA): Dept. of Statistics, Stanford University; 1969. Technical Report #150.
  • Pabst B, Vicentini H. Dislocation experiments in the migrating sea star Astropecten jonstoni. Mar Biol. 1978;48:271–278. doi: 10.1007/BF00397154

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