×

A Bayesian analysis of the change-point problem for directional data. (English) Zbl 1147.62024

Summary: We discuss a simple fully Bayesian analysis of the change-point problem for directional data in the parametric framework with von Mises or circular normal distributions as the underlying distribution. We first discuss the problem of detecting change in the mean direction of the circular normal distribution using a latent variable approach when the concentration parameter is unknown. Then, a simpler approach, beginning with proper priors for all the unknown parameters - the sampling importance resampling technique - is used to obtain the posterior marginal distribution of the change-point.
The method is illustrated using wind data [E. P. Weijers, A. Van Delden, H. F. Vugts and A. G. C. A. Meesters, The composite horizontal wind field within convective structures of the atmospheric surface layer. J. Atmos. Sci. 52, 3866–3878 (1995)]. The method can be adapted for a variety of situations involving both angular and linear data and can be used with profit in the context of statistical process control in Phase I of control charting and also in Phase II in conjunction with control charts.

MSC:

62F15 Bayesian inference
62H11 Directional data; spatial statistics
62P12 Applications of statistics to environmental and related topics
86A10 Meteorology and atmospheric physics

Software:

DDSTAP
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Chen J., Parametric Statistical Change Point Analysis (2000) · Zbl 0980.62013
[2] DOI: 10.1214/aoms/1177700517 · Zbl 0218.62033
[3] DOI: 10.2307/3315639 · Zbl 0941.62062
[4] DOI: 10.1093/biomet/57.1.1 · Zbl 0198.51501
[5] DOI: 10.1142/9789812779267
[6] Laha A. K., Slippage and Change Point Problems with Directional Data (2001)
[7] Laha, A. K. 2002.Control charts for angular observations, in Statistical Methods for Quality ImprovementEdited by: Aich, A. B., Chatterjee, A. and Chattopadhyay, A. K. 39–45. IAPQR, Kolkata
[8] Laha A. K., Statist. Methods 5 pp 31– (2003)
[9] DOI: 10.2307/1268988 · Zbl 0616.62059
[10] Page E. S., Biometrika 42 pp 523– (1955)
[11] Sen A. K., Sankhya A 35 pp 173– (1973)
[12] DOI: 10.1214/aos/1176343001 · Zbl 0305.62014
[13] DOI: 10.2307/1268001 · Zbl 0294.62023
[14] SenGupta A., DDSTAP – A Statistical Analysis Package for Directional Data (1996)
[15] SenGupta A., DDSTAP 1.1 – A Statistical Analysis Package for Directional Data (updated) (2005)
[16] SenGupta A., Change-point tests for the mean direction in the presence of general nuisance parameters (2006)
[17] DOI: 10.2307/2684170 · Zbl 04510712
[18] DOI: 10.2307/2669484
[19] DOI: 10.1175/1520-0469(1995)052<3866:TCHWFW>2.0.CO;2
[20] Woodall W. H., J. Qual. Technol. 31 pp 376– (1999)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.