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We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions. We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models,…
Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter $\theta$ approaches infinity. The motivation for these results is to understand the…
Probabilistic finite mixture models are widely used for unsupervised clustering. These models can often be improved by adapting them to the topology of the data. For instance, in order to classify spatially adjacent data points similarly,…
We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights.…
A reparametrized Dirichlet-multinomial distribution is introduced, and the covariance matrix, as well as, the algorithm for calculating the PDF for n species are provided. The distribution is suited for modelling the joint distribution of…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
The computation of two Bayesian predictive distributions which are discrete mixtures of incomplete beta functions is considered. The number of iterations can easily become large for these distributions and thus, the accuracy of the result…
The mean residual life function is a key functional for a survival distribution. It has a practically useful interpretation as the expected remaining lifetime given survival up to a particular time point, and it also characterizes the…
When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models…
Combining the outputs of multiple classifiers or experts into a single probabilistic classification is a fundamental task in machine learning with broad applications from classifier fusion to expert opinion pooling. Here we present a…
The behavior of the Poisson-Dirichlet distribution with small mutation rate is studied through large deviations. The structure of the rate function indicates that the number of alleles is finite at the instant when mutation appears. The…
The advent of Generative Artificial Intelligence (GAI) has heralded an inflection point that changed how society thinks about knowledge acquisition. While GAI cannot be fully trusted for decision-making, it may still provide valuable…
We consider an array of random variables, taking values in a complete and separable metric space, that exhibits a kind of symmetry which we call row exchangeability. Given such an array, a natural model for Bayesian nonparametric inference…
The study of properties of mean functionals of random probability measures is an important area of research in the theory of Bayesian nonparametric statistics. Many results are now known for random Dirichlet means, but little is known,…
We consider the challenges that arise when fitting complex ecological models to 'large' data sets. In particular, we focus on random effect models which are commonly used to describe individual heterogeneity, often present in ecological…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
In this paper we present a flexible bivariate distribution specified by a quantile function. The distribution contains as special cases new bivariate exponential, Pareto I, Pareto II, beta, power, log logistic and uniform distributions and…
Bayesian model averaging, model selection and its approximations such as BIC are generally statistically consistent, but sometimes achieve slower rates og convergence than other methods such as AIC and leave-one-out cross-validation. On the…
Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…
In Bayesian meta-analysis, the specification of prior probabilities for the between-study heterogeneity is commonly required, and is of particular benefit in situations where only few studies are included. Among the considerations in the…