Bayesian nonparametrics

The Bayesian approach to nonparametric statistics (see parametric versus nonparametric statistics). We replace the finite dimensional model in Bayesian parametrics (e.g., $\{f_{\theta }:\theta \in \Theta \}$ where $\Theta$ has finite dimensions) with an infinite dimensional model, such as the class of all square integrable functions.

Examples of some common Bayesian nonparametric methods:

• Gaussian process regression for nonparametric regression
• Dirichlet process mixture for nonparametric density estimation
• Dirichlet process for cdf estimation.