A Bayesian Analysis of the Change Point Problem for Directional Data using SIR
Abstract
In this paper we discuss a simple fully Bayesian analysis of the change point
problem for the directional data in the parametric framework with circular
normal distribution as the underlying distribution. We discuss the problem of
detecting change in the mean direction of the circular normal distribution when
the concentration parameter is unknown. Beginning with proper priors for all
the unknown parameters, the sampling-importance-resampling (SIR)
technique is used to obtain the posterior marginal distribution of the change
point. The method is illustrated using the wind data (Weijer‘s et. al.(1995)).
The method can be adapted to 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.
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