On selecting the hyperparameters of the DPM models for the density estimation of observation errors

The Dirichlet Process Mixture (DPM) models represent an attractive approach to modeling latent distributions parametrically. In DPM models the Dirichlet process (DP) is applied especially when the distribution of latent parameters is to be considered as multimodal. DPMs allow for uncertainty in the choice of parametric forms and in the number of mixing components (clusters). The parameters of a DP include the precision a and the base probability measure G₀(μ, Σ). In most applications, the choice of priors and posteriors computation for the hyperparameters (α, μ, Σ) clearly influences inferences about the level of clustering in the mixture. This is the main focus of this paper. We consider the problem of density estimation of an observation noise distribution in a dynamic nonlinear model from a Bayesian nonparametric view-point. Our approach is illustrated in a real-world data analysis task dealing with the estimation of pseudorange errors in a GNSS based localization context.