Room D3-2019, 2500 Boul. de l'Université, Sherbrooke, QC, J1K 2R1, CA
A circular analogue to the Bernstein polynomial densities
Normalized Bernstein polynomials have been widely used for the mixturemodelling of density functions supported on the interval. They enable to relatethe geometry of the density to the mixture weights in simple and interpretableterms. This has led, in particular, to their use for monotone, unimodal andcopula density estimation. We present a trigonometric counterpart to the Bernstein polynomial den-sities which is adapted to circular domains and accounts for the wrapping ofangular data. Properties relevant to its application are studied and we givesimple conditions on weights for the resulting mixture to be either periodicallyunimodal or symmetric. We consider random polynomial priors based on thisbasis and show that, for circular density estimation, posterior means comparesfavourably to other methods previously suggested in the literature. Strong pos-terior consistency is obtained for a wide class of densities and we briefly revisitthe issue of posterior simulation. Joint work with Simon Guillotte.