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In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…
A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…
We construct an infinitely exchangeable process on the set $\cate$ of subsets of the power set of the natural numbers $\mathbb{N}$ via a Poisson point process with mean measure $\Lambda$ on the power set of $\mathbb{N}$. Each $E\in\cate$…
Bayesian latent space models offer a principled approach to network representation, but rely on correct specification of both geometry and link function. Real-world networks often violate these assumptions, exhibiting geometric mismatch and…
Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes…
The proposal and study of dependent prior processes has been a major research focus in the recent Bayesian nonparametric literature. In this paper, we introduce a flexible class of dependent nonparametric priors, investigate their…
We construct a novel class of stochastic blockmodels using Bayesian nonparametric mixtures. These model allows us to jointly estimate the structure of multiple networks and explicitly compare the community structures underlying them, while…
Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular,…
The human ability to flexibly reason using analogies with domain-general content depends on mechanisms for identifying relations between concepts, and for mapping concepts and their relations across analogs. Building on a recent model of…
We present a comprehensive extension of the latent position network model known as the random dot product graph to accommodate multiple graphs -- both undirected and directed -- which share a common subset of nodes, and propose a method for…
Traditional Bayesian random partition models assume that the size of each cluster grows linearly with the number of data points. While this is appealing for some applications, this assumption is not appropriate for other tasks such as…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
A sequence of random variables is exchangeable if its joint distribution is invariant under variable permutations. We introduce exchangeable variable models (EVMs) as a novel class of probabilistic models whose basic building blocks are…
In this article, we propose a new class of priors for Bayesian inference with multiple Gaussian graphical models. We introduce fully Bayesian treatments of two popular procedures, the group graphical lasso and the fused graphical lasso, and…
Bayesian statistical models allow us to formalise our knowledge about the world and reason about our uncertainty, but there is a need for better procedures to accurately encode its complexity. One way to do so is through compositional…
Graphical model learning and inference are often performed using Bayesian techniques. In particular, learning is usually performed in two separate steps. First, the graph structure is learned from the data; then the parameters of the model…
In this paper we propose a Bayesian nonparametric approach to modelling sparse time-varying networks. A positive parameter is associated to each node of a network, which models the sociability of that node. Sociabilities are assumed to…
We present a flexible Bayesian semiparametric mixed model for longitudinal data analysis in the presence of potentially high-dimensional categorical covariates. Building on a novel hidden Markov tensor decomposition technique, our proposed…
Consider observations $y_1,\dots,y_n$ on nodes of a connected graph, where the $y_i$ independently come from $N(\theta_i, \sigma^2)$ distributions and an unknown partition divides the $n$ observations into blocks. One well-studied class of…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…