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We propose alternatives to Bayesian a priori distributions that are frequently used in the study of inverse problems. Our aim is to construct priors that have similar good edge-preserving properties as total variation or Mumford-Shah priors…

Bayesian analyses combine information represented by different terms in a joint Bayesian model. When one or more of the terms is misspecified, it can be helpful to restrict the use of information from suspect model components to modify…

This paper introduces the concept of random context representations for the transition probabilities of a finite-alphabet stochastic process. Processes with these representations generalize context tree processes (a.k.a. variable length…

Bayesian regression trees are flexible non-parametric models that are well suited to many modern statistical regression problems. Many such tree models have been proposed, from the simple single- tree model to more complex tree ensembles.…

We present an analysis of parton distribution functions (PDFs) of the proton using Markov Chain Monte Carlo (MCMC) methods. The MCMC approach naturally implements Bayes' theorem and thus provides a means to directly sample the underlying…

Estimating the effective sample size (ESS) is fundamental in Bayesian phylogenetic inference to properly account for autocorrelation in MCMC samples. While methods for continuous parameters are well established, the discrete and…

Determining potential probability distributions with a given causal graph is vital for causality studies. To bypass the difficulty in characterizing latent variables in a Bayesian network, the nested Markov model provides an elegant…

We describe an adaptive context tree weighting (ACTW) algorithm, as an extension to the standard context tree weighting (CTW) algorithm. Unlike the standard CTW algorithm, which weights all observations equally regardless of the depth, ACTW…

We consider sequences of tree-valued Markov chains that describe evolving genealogies in Cannings models, and we show their convergence in distribution to tree-valued Fleming-Viot processes. Under the conditions of M\"ohle and Sagitov, this…

We consider deep neural networks in a Bayesian framework with a prior distribution sampling the network weights at random. Following a recent idea of Agapiou and Castillo (2023), who show that heavy-tailed prior distributions achieve…

We propose prior distributions for all parts of the specification of a Markov mesh model. In the formulation we define priors for the sequential neighborhood, for the parametric form of the conditional distributions and for the parameter…

Supervised classification is one of the most ubiquitous tasks in machine learning. Generative classifiers based on Bayesian networks are often used because of their interpretability and competitive accuracy. The widely used naive and TAN…

Rooted bifurcating trees are mathematical objects used to model evolutionary relationships and arise naturally in both coalescent theory and phylogenetics. Recent numerical representations of tree topologies, known as F-matrices, allow for…

We introduce a new class of lower bounds on the log partition function of a Markov random field which makes use of a reversed Jensen's inequality. In particular, our method approximates the intractable distribution using a linear…

We develop a multilevel Monte Carlo (MLMC)-FEM algorithm for linear, elliptic diffusion problems in polytopal domain $\mathcal D\subset \mathbb R^d$, with Besov-tree random coefficients. This is to say that the logarithms of the diffusion…

Low-dimensional probability models for local distribution functions in a Bayesian network include decision trees, decision graphs, and causal independence models. We describe a new probability model for discrete Bayesian networks, which we…

Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…

We prove complex contraction for zero-free regions of counting weighted set cover problem in which an element can appear in an unbounded number of sets, thus obtaining fully polynomial-time approximation schemes(FPTAS) via Barvinok's…

Bayesian networks are popular probabilistic models that capture the conditional dependencies among a set of variables. Inference in Bayesian networks is a fundamental task for answering probabilistic queries over a subset of variables in…

Weighted model integration (WMI) extends Weighted model counting (WMC) to the integration of functions over mixed discrete-continuous domains. It has shown tremendous promise for solving inference problems in graphical models and…