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Burton Wu
Clare A. McGrory
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Anthony N. Pettitt


The emerging variational Bayesian (VB) technique for approximate Bayesian statistical inference is a non-simulation-based and time-efficient approach. It provides a useful, practical alternative to other Bayesian statistical approaches such as Markov chain Monte Carlo–based techniques, particularly for applications involving large datasets. This article reviews the increasingly popular VB statistical approach and illustrates how it can be used to fit Gaussian mixture models to circular wave direction data. This is done by taking the straightforward approach of padding the data; this method involves adding a repeat of a complete cycle of the data to the existing dataset to obtain a dataset on the real line. The padded dataset can then be analyzed using the standard VB technique. This results in a practical, efficient approach that is also appropriate for modeling other types of circular, or directional, data such as wind direction.

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