On sufficient conditions for Bayesian consistency

This paper contributes to the theory of Bayesian consistency for a sequence of posterior and predictive distributions arising from an independent and identically distributed sample. A new sufficient condition for posterior Hellinger consistency is presented which provides motivation for recent results appearing in the literature. Such motivation is important since current sufficient conditions are not known to be necessary. It also provides new insights into Bayesian consistency. A new consistency theorem for the sequence of predictive densities is given.