Bayesian Nonparametrics for Directional Statistics
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A density basis of the trigonometric polynomials, suitable for mixture modelling, is introduced. Statistical and geometric properties are derived, suggesting it as a circular analogue to the Bernstein polynomial densities. Nonparametric priors are constructed and strong posterior consistency is obtained for a wide class of densities. We conclude by comparing posterior mean estimates to other circular density estimation methods, also based on trigonometric polynomials, previously suggested in the literature.
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