Tractable circula densities from Fourier series

This article proposes an approach, based on infinite Fourier series, to constructing tractable densities for the bivariate circular analogues of copulas recently coined ‘circulas’. As examples of the general approach, we consider circula densities generated by various patterns of nonzero Fourier coefficients. The shape and sparsity of such arrangements are found to play a key role in determining the properties of the resultant models. The special cases of the circula densities we consider all have simple closed-form expressions involving no computationally demanding normalizing constants and display wide-ranging distributional shapes. A highly successful model identification tool and methods for parameter estimation and goodness-of-fit testing are provided for the circula densities themselves and the bivariate circular densities obtained from them using a marginal specification construction. The modelling capabilities of such bivariate circular densities are compared with those of five existing models in a numerical experiment, and their application illustrated in an analysis of wind directions.

bridgesampling: An R Package for Estimating Normalizing Constants

Statistical procedures such as Bayes factor model selection and Bayesian model averaging require the computation of normalizing constants (e.g., marginal likelihoods). These normalizing constants are notoriously difficult to obtain, as they usually involve high-dimensional integrals that cannot be solved analytically. Here we introduce an R package that uses bridge sampling (Meng and Wong 1996; Meng and Schilling 2002) to estimate normalizing constants in a generic and easy-to-use fashion. For models implemented in Stan, the estimation procedure is automatic. We illustrate the functionality of the package with three examples.