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We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic…
A large amount of observational data has been accumulated in various fields in recent times, and there is a growing need to estimate the generating processes of these data. A linear non-Gaussian acyclic model (LiNGAM) based on the…
We consider the problem of learning parameters of latent variable models from mixed (continuous and ordinal) data with missing values. We propose a novel Bayesian Gaussian copula factor (BGCF) approach that is consistent under certain…
Graphical models are an important tool in exploring relationships between variables in complex, multivariate data. Methods for learning such graphical models are well developed in the case where all variables are either continuous or…
A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…
While Robert and Rousseau (2010) addressed the foundational aspects of Bayesian analysis, the current chapter details its practical aspects through a review of the computational methods available for approximating Bayesian procedures.…
We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a…
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
We introduce a new category of multivariate conditional generative models and demonstrate its performance and versatility in probabilistic time series forecasting and simulation. Specifically, the output of quantile regression networks is…
This paper is a note on the use of Bayesian nonparametric mixture models for continuous time series. We identify a key requirement for such models, and then establish that there is a single type of model which meets this requirement. As it…
State estimation of dynamical systems is crucial for providing new decision-making and system automation information in different applications. However, the assumptions on the standard computational models for sensor measurements can be…
Bayesian aggregation lets election forecasters combine diverse sources of information, such as state polls and economic and political indicators: as in our collaboration with The Economist magazine. However, the demands of real-time…
In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
There has been considerable recent interest in Bayesian modeling of high-dimensional networks via latent space approaches. When the number of nodes increases, estimation based on Markov Chain Monte Carlo can be extremely slow and show poor…
Probabilistic modeling of multidimensional spatiotemporal data is critical to many real-world applications. As real-world spatiotemporal data often exhibits complex dependencies that are nonstationary and nonseparable, developing effective…
We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for…
Optimal design facilitates intelligent data collection. In this paper, we introduce a fully Bayesian design approach for spatial processes with complex covariance structures, like those typically exhibited in natural ecosystems. Coordinate…
The Bayes factor, the data-based updating factor from prior to posterior odds, is a principled measure of relative evidence for two competing hypotheses. It is naturally suited to sequential data analysis in settings such as clinical trials…