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Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…

Bayesian Optimization is methodology used in statistical modelling that utilizes a Gaussian process prior distribution to iteratively update a posterior distribution towards the true distribution of the data. Finding unbiased informative…

Causal discovery is crucial for understanding complex systems and informing decisions. While observational data can uncover causal relationships under certain assumptions, it often falls short, making active interventions necessary. Current…

Gathering labeled data to train well-performing machine learning models is one of the critical challenges in many applications. Active learning aims at reducing the labeling costs by an efficient and effective allocation of costly labeling…

Several approaches have been proposed in the literature for clustering multivariate ordinal data. These methods typically treat missing values as absent information, rather than recognizing them as valuable for profiling population…

Bayesian optimization (BO) is a powerful and data-efficient method for iterative materials discovery and design, particularly valuable when prior knowledge is limited, underlying functional relationships are complex or unknown, and the cost…

In the analysis of observational data in social sciences and businesses, it is difficult to obtain a "(quasi) single-source dataset" in which the variables of interest are simultaneously observed. Instead, multiple-source datasets are…

Motivated by distinct walking patterns in real-world free-living gait data, this paper proposes an innovative curve-based sampling scheme for the analysis of functional data characterized by a mixture of covariance structures. Traditional…

We propose a practical Bayesian optimization method using Gaussian process regression, of which the marginal likelihood is maximized where the number of model selection steps is guided by a pre-defined threshold. Since Bayesian optimization…

Accurate estimation of error covariances (both background and observation) is crucial for efficient observation compression approaches in data assimilation of large-scale dynamical problems. We propose a new combination of a covariance…

Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…

State estimation for nonlinear state space models (SSMs) is a challenging task. Existing assimilation methodologies predominantly assume Gaussian posteriors on physical space, where true posteriors become inevitably non-Gaussian. We propose…

Aggregated data is commonplace in areas such as epidemiology and demography. For example, census data for a population is usually given as averages defined over time periods or spatial resolutions (cities, regions or countries). In this…

Meta-analysis is widely used to integrate results from multiple experiments to obtain generalized insights. Since meta-analysis datasets are often heteroscedastic due to varying subgroups and temporal heterogeneity arising from experiments…

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…

We explore the performance of sample average approximation in comparison with several other methods for stochastic optimization when there is information available on the underlying true probability distribution. The methods we evaluate are…

Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…

We consider Bayesian optimization of the output of a network of functions, where each function takes as input the output of its parent nodes, and where the network takes significant time to evaluate. Such problems arise, for example, in…

Data assimilation (DA) aims at forecasting the state of a dynamical system by combining a mathematical representation of the system with noisy observations taking into account their uncertainties. State of the art methods are based on the…

Given a decision process based on the approximate probability density function returned by a data assimilation algorithm, an interaction level between the decision making level and the data assimilation level is designed to incorporate the…