A Circular Analogue to the Bernstein Polynomial Densities, Bayesian Nonparametrics and Large Support Asymptotics
The use of truncated Fourier series in circular distribution modelling has been criticized for the lack of control it provides. To address this problem, we suggest a density basis of the trigonometric polynomials that is analogous to the Bernstein polynomial densities. We demonstrate key properties that allow the specification of shape constraints and the efficient simulation of the resulting trigonometric densities. For the purpose of density estimation, we consider random polynomial priors built from this basis and show that posterior means compare favourably to other density estimates previously suggested in the literature. We give a new result on the Kullback-Leibler support of sieve priors that ensures posterior consistency in the estimation of discontinuous densities while known results, valid under regularity assumptions, complete the asymptotic picture. Joint work with Simon Guillotte.