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Predicting the winner of an election is of importance to multiple stakeholders. To formulate the problem, we consider an independent sequence of categorical data with a finite number of possible outcomes in each. The data is assumed to be…
Latent Dirichlet allocation (LDA) is an important hierarchical Bayesian model for probabilistic topic modeling, which attracts worldwide interests and touches on many important applications in text mining, computer vision and computational…
Ranking, and inferences based on ranking of a set of entities, are important problems in numerous contexts. This is especially true in small area statistics where there may be only a limited amount of directly observed data from each entity…
We revisit the Bayesian Context Trees (BCT) modelling framework for discrete time series, which was recently found to be very effective in numerous tasks including model selection, estimation and prediction. A novel representation of the…
We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…
We propose a method to improve the efficiency and accuracy of amortized Bayesian inference by leveraging universal symmetries in the joint probabilistic model of parameters and data. In a nutshell, we invert Bayes' theorem and estimate the…
The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…
We propose a geometric algorithm for topic learning and inference that is built on the convex geometry of topics arising from the Latent Dirichlet Allocation (LDA) model and its nonparametric extensions. To this end we study the…
The measurement of the efficiency of an event selection is always an important part of the analysis of experimental data. The statistical techniques which are needed to determine the efficiency and its uncertainty are reviewed. Frequentist…
As for other latent-variable problems, exact Bayesian analysis is typically not practicable for mixture problems and approximate methods have been developed. Variational Bayes tends to produce approximate posterior distributions for…
Latent Dirichlet Allocation (LDA) is a foundational model for discovering latent thematic structure in discrete data, but its Dirichlet prior cannot represent the rich correlations and hierarchical relationships often present among topics.…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
We investigate the problem of semi-parametric maximum likelihood under constraints on summary statistics. Such a procedure results in a discrete probability distribution that maximises the likelihood among all such distributions under the…
Consider the random Dirichlet partition of the interval into $n$ fragments with parameter $\theta >0$. We recall the unordered Ewens sampling formulae from finite Dirichlet partitions. As this is a key variable for estimation purposes,…
This work is motivated by the analysis of ecological interaction networks. Poisson stochastic blockmodels are widely used in this field to decipher the structure that underlies a weighted network, while accounting for covariate effects.…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
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…
We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can…
We provide a new characterization of the Dirichlet distribution. This characterization implies that under assumptions made by several previous authors for learning belief networks, a Dirichlet prior on the parameters is inevitable.
The analysis of rank ordered data has a long history in the statistical literature across a diverse range of applications. In this paper we consider the Extended Plackett-Luce model that induces a flexible (discrete) distribution over…