Sequential Monte Carlo methods for mixtures with normalized random measures with independent increments priors

Normalized random measures with independent increments are a general, tractable class of nonparametric prior. This paper describes sequential Monte Carlo methods for both conjugate and non-conjugate nonparametric mixture models with these priors. A simulation study is used to compare the efficiency of the different algorithms for density estimation. The methods are further illustrated by application to estimation of the marginal likelihood in a goodness-of-fit testing example and to fitting a nonparametric stochastic volatility model.