## AbstractBayesian nonparametric models can be regarded as Bayesian models on infinite-dimensional spaces. These infinite-dimensional distributions can be constructed from finite-dimensional ones using the tools of stochastic process theory. An example is the construction of the Gaussian process constructed from Gaussian distributions. My talk will address the question which finite-dimensional distributions are suitable for the construction of nonparametric Bayesian models with useful statistical properties. By a proper choice of finite-dimensional models used in the construction, the nonparametric Bayesian model can be guaranteed to be conjugate, and to have a sufficient statistic. I will briefly discuss for which models these constructions follow a generic recipe, and for which cases we have to expect mathematical complications.
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