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We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian Structural Inference (BSI) relies on a set of candidate unifilar HMM (uHMM) topologies for inference of process…

Stochastic volatility models are the backbone of financial engineering. We study both continuous time diffusions as well as discrete time models. We propose two novel approaches to estimating stochastic volatility diffusions, one using…

Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…

In this work, we present a new class of models, called uncertain-input models, that allows us to treat system-identification problems in which a linear system is subject to a partially unknown input signal. To encode prior information about…

Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…

Bayesian network classifiers (BNCs) possess a number of properties desirable for a modern classifier: They are easily interpretable, highly scalable, and offer adaptable complexity. However, traditional methods for learning BNCs have…

We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…

Pairwise Markov Models (PMMs) extend the wellknown Hidden Markov Models (HMMs). Being significantly more general, PMMs enable several types of processing, like Bayesian filtering or smoothing, similar to those used in HMMs. In this paper,…

Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the…

Purpose: Machine learning is broadly used for clinical data analysis. Before training a model, a machine learning algorithm must be selected. Also, the values of one or more model parameters termed hyper-parameters must be set. Selecting…

This paper investigates asset allocation problems when returns are predictable. We introduce a market-timing Bayesian hierarchical (BH) approach that adopts heterogeneous time-varying coefficients driven by lagged fundamental…

This article presents new methodology for sample-based Bayesian inference when data are partitioned and communication between the parts is expensive, as arises by necessity in the context of "big data" or by choice in order to take…

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…

The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. Importance sampling formulas take on an easy form relating to the deviance in exponential families and are particularly simple starting…

Finding the model that best describes a high-dimensional dataset is a daunting task, even more so if one aims to consider all possible high-order patterns of the data, going beyond pairwise models. For binary data, we show that this task…

In the big data era, scalability has become a crucial requirement for any useful computational model. Probabilistic graphical models are very useful for mining and discovering data insights, but they are not scalable enough to be suitable…

This paper examines Bayesian belief network inference using simulation as a method for computing the posterior probabilities of network variables. Specifically, it examines the use of a method described by Henrion, called logic sampling,…

Comparison of appropriate models to describe observational data is a fundamental task of science. The Bayesian model evidence, or marginal likelihood, is a computationally challenging, yet crucial, quantity to estimate to perform Bayesian…

Hierarchical time series forecasting plays a crucial role in decision-making in various domains while presenting significant challenges for modelling as they involve multiple levels of aggregation, constraints, and availability of…

Prior information often takes the form of parameter constraints. Bayesian methods include such information through prior distributions having constrained support. By using posterior sampling algorithms, one can quantify uncertainty without…