We discuss the relevance of consistency to the Bayesian. Should consistency be dismissed as irrelevant or thought about seriously when constructing prior distributions? Strong opinions have been held on this matter, but it is probably fair to say it is a largely neglected area. Pioneers, such as...

This paper studies a novel idea for constructing continuous-time stationary Markov models. The approach undertaken is based on a latent representation of the corresponding transition probabilities that conveys to appealing ways to study and simulate the dynamics of the constructed processes....

This paper introduces a new family of Bayesian semi-parametric models for the conditional distribution of daily stock index returns. The proposed models capture key stylized facts of such returns, namely heavy tails, asymmetry, volatility clustering, and leverage. A Bayesian nonparametric prior...

An approach to constructing strictly stationary AR(1)-type models with arbitrary stationary distributions and a flexible dependence structure is introduced. Bayesian nonparametric predictive density functions, based on single observations, are used to construct the one-step ahead predictive...