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Bayesian models based on the Dirichlet process and other stick-breaking priors have been proposed as core ingredients for clustering, topic modeling, and other unsupervised learning tasks. Prior specification is, however, relatively difficult for such models, given that their flexibility implies that the consequences of prior choices are often relatively opaque. Moreover, these choices can have a substantial effect on posterior inferences. Thus, considerations of robustness need to go hand in hand with nonparametric modeling. In the current paper, we tackle this challenge by exploiting the fact that variational Bayesian methods, in addition to having computational advantages in fitting complex nonparametric models, also yield sensitivities with respect to parametric and nonparametric aspects of Bayesian models. In particular, we demonstrate how to assess the sensitivity of conclusions to the choice of concentration parameter and stick-breaking distribution for inferences under Dirichlet process mixtures and related mixture models. We provide both theoretical and empirical support for our variational approach to Bayesian sensitivity analysis.
The vast majority of models for the spread of communicable diseases are parametric in nature and involve underlying assumptions about how the disease spreads through a population. In this article we consider the use of Bayesian nonparametric approach
We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet distributi
This preprint has been reviewed and recommended by Peer Community In Evolutionary Biology (http://dx.doi.org/10.24072/pci.evolbiol.100036). Approximate Bayesian computation (ABC) has grown into a standard methodology that manages Bayesian inference f
A large number of statistical models are doubly-intractable: the likelihood normalising term, which is a function of the model parameters, is intractable, as well as the marginal likelihood (model evidence). This means that standard inference techniq
Approximate Bayesian Computation (ABC) methods are used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Both the accuracy and computational efficiency of ABC depend on the choice of summary st