A flexible Bayesian mixture approach for multi-modal circular data

Yıl 2022, Cilt: 51 Sayı: 4, 1160 - 1173, 01.08.2022

Muhammet Burak Kılıç Zeynep Kalaylıoğlu Ashıs Sengupta

https://doi.org/10.15672/hujms.897144

Cited By: 1

Öz

In this article, we consider multi-modal circular data and nonparametric inference. We introduce a doubly flexible method based on Dirichlet process circular mixtures in which parameter assumptions are relaxed. We assess and discuss in simulation studies the efficiency of the proposed extension relative to the standard finite mixture applications in the analysis of multi-modal circular data. The real data application shows that this relaxed approach is promising for making important contributions to our understanding of many real-life phenomena particularly in environmental sciences such as animal orientations.

Anahtar Kelimeler

directional data, Dirichlet process prior, mixture models, stick breaking construction, animal orientation

Kaynakça

• [1] C. Agostinelli and U. Lund, R package ’circular’: Circular Statistics (version 0.4-93), 2017.
• [2] S. Akesson, R. Klaassen, J. Holmgren, J.W. Fox and A. Hedenstrom, Migration routes and strategies in a highly aerial migrant, the common swift Apus apus, revealed by light-level geolocators, PLoS One 7 (7), 1-9, 2012.
• [3] C.E. Antoniak, Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems, Ann. Statist. 2 (6), 1152-1174, 1974.
• [4] S. Bhattacharya, and A. SenGupta, Bayesian analysis of semiparametric linearcircular models, J. Agric. Biol. Environ. Stat. 14 (1), 33-65, 2009.
• [5] T. Ferguson, A Bayesian analysis of some non-parametric problems, Ann. Statist. 1 (2), 209-230, 1973.
• [6] N.I. Fisher, Statistical Analysis of Circular Data, Cambridge University Press, 1993.
• [7] M.D. Fraser, H. Yu-Sheng and J.J. Walker, Identifiability of finite mixtures of von Mises distributions, Ann. Statist. 9 (5), 1130-1131, 1981.
• [8] R. Gatto and S.R. Jammalamadaka, The generalized von Mises distribution, Stat. Methodol. 4 (3), 341-353, 2007.
• [9] K. Ghosh, S.R. Jammalamadaka and R. Tiwari, Semiparametric Bayesian techniques for problems in circular data, J. Appl. Stat. 30 (2), 145-161, 2003.
• [10] T. Guilford, R. Freeman, D. Boyle, B. Dean, H. Kirk, R. Phillips and C. Perrins, A dispersive migration in the Atlantic puffin and its implications for migratory navigation, PLoS One 6 (7), 1-8, 2011.
• [11] E.J. Gumbel, Applications of the circular normal distribution, J. Amer. Statist. Assoc. 49 (266), 267-297, 1954.
• [12] H. Holzmann, A. Munk and B. Stratmann, Identifiability of finite mixtures - with applications to circular distributions, Sankhya 66 (3), 440-449, 2004.
• [13] K. Hornik, I. Feinerer, M. Kober and C. Buchta, Spherical k-means clustering, J. Stat. Softw. 50 (10), 1-22, 2012.
• [14] H. Ishwaran and L.F. James, Approximate Dirichlet process computing in finite normal mixtures: smoothing and prior information, J. Comput. Graph. Statist. 11 (3), 508-532, 2002.
• [15] S.R. Jammalamadaka, B. Wainwright and Q. Jin, Functional clustering on a circle using von Mises mixtures, J. Stat. Theory Pract. 15 (2), 1-17, 2021.
• [16] T.A. Jones and W.R. James, Analysis of bimodal orientation data, J. Int. Assoc. Math. Geol. 1 (2), 129-135, 1969.
• [17] S. Kim and A. SenGupta, A three-parameter generalized von Mises distribution, Statist. Papers 54 (3), 685-693, 2013.
• [18] K.V. Mardia, Statistics of directional data, J. R. Stat. Soc. Ser. B. Stat. Methodol. 37 (3), 349–393, 1975.
• [19] K.V. Mardia and T.W. Sutton, On the modes of a mixture of two von Mises distributions, Biometrika 62 (3), 699-701, 1975.
• [20] R.M. Neal, Markov chain sampling methods for Dirichlet process mixture models, J. Comput. Graph. Statist. 9 (2), 249-265, 2000.
• [21] G. Nunez-Antonio, M.C. Ausin and M.P. Wiper, Bayesian nonparametric models of circular variables based on Dirichlet process mixtures of normal distributions, J. Agric. Biol. Environ. Stat. 20 (1), 47-64, 2015.
• [22] G. Nunez-Antonio, M. Mendoza, A. Contreras-Cristan, E. Gutierrez-Pena and E. Mendoza, Bayesian nonparametric inference for the overlap of daily animal activity patterns, Environ. Ecol. Stat. 25 (4), 471-494, 2018.
• [23] A. Ożarowska, M. Ilieva, P. Zehtindjiev, S. Akesson and K. Muś, A new approach to evaluate multimodal orientation behaviour of migratory passerine birds recorded in circular orientation cages, J. Exp. Biol. 216 (21), 4038-4046, 2013.
• [24] A. Pewsey, The wrapped stable family of distributions as a flexible model for circular data, Comput. Statist. Data Anal. 52 (3), 1516-1523, 2008.
• [25] J.R. Pcyke, Some tests for uniformity of circular distributions powerful against multimodal alternatives, Canad. J. Statist. 38 (1), 80-96, 2010.
• [26] A. SenGupta and M. Roy, Clustering on the torus, J. Stat. Theory Pract. 15 (3), 1-18, 2021.
• [27] A. SenGupta, M. Roy and A.K. Chattopadhyay, Model-based clustering for cylindrical data, in: I. Ghosh, N. Balakrishnan, H.K.T. Ng (ed.) Advances in Statistics - Theory and Applications, Emerging Topics in Statistics and Biostatistics, 347-363, Springer, Cham, 2021.
• [28] J. Sethuraman, A constructive definition of Dirichlet priors, Statist. Sinica 4 (2), 639-650, 1994.
• [29] M.A. Stephens, Techniques for directional data, Technical Report 150, Stanford University, Department of Statistics, 1969.
• [30] S. Sturtz, U. Ligges and A. Gelman, R2WinBUGS: A Package for running WinBUGS from R, J. Stat. Softw. 12 (3), 1-16, 2005.
• [31] E.A. Yfantis and L.E. Borgman, An extension of the von Mises distribution, Comm. Statist. Theory Methods 11 (15), 1695-1706, 1982.