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Ordinary differential equations (ODEs) can provide mechanistic models of temporally local changes of processes, where parameters are often informed by external knowledge. While ODEs are popular in systems modeling, they are less established…

Conditional density estimation is complicated by multimodality, heteroscedasticity, and strong non-Gaussianity. Gaussian processes (GPs) provide a principled nonparametric framework with calibrated uncertainty, but standard GP regression is…

Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean vector and the between-study covariance…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…

Detection heterogeneity is inherent to ecological data, arising from factors such as varied terrain or weather conditions, inconsistent sampling effort, or heterogeneity of individuals themselves. Incorporating additional covariates into a…

Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…

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…

Generating realistic training data for supervised learning remains a significant challenge in artificial intelligence, particularly in domains where large, expert-labeled datasets are scarce or costly to obtain. This is especially true for…

Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…

This paper introduces a non-parametric estimation algorithm designed to effectively estimate the joint distribution of model parameters with application to population pharmacokinetics. Our research group has previously developed the…

Often the regression function appearing in fields like economics, engineering, biomedical sciences obeys a system of higher order ordinary differential equations (ODEs). The equations are usually not analytically solvable. We are interested…

Predicated on the increasing abundance of electronic health records, we investi- gate the problem of inferring individualized treatment effects using observational data. Stemming from the potential outcomes model, we propose a novel multi-…

Acoustic modeling serves audio processing tasks such as de-noising, data reconstruction, model-based testing and classification. Previous work dealt with signal parameterization of wave envelopes either by multiple Gaussian distributions or…

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,…

The doubly robust estimator, which models both the propensity score and outcomes, is a popular approach to estimate the average treatment effect in the potential outcome setting. The primary appeal of this estimator is its theoretical…

Prototypical-part methods, e.g., ProtoPNet, enhance interpretability in image recognition by linking predictions to training prototypes, thereby offering intuitive insights into their decision-making. Existing methods, which rely on a…

Motivated by many application problems, we consider Markov decision processes (MDPs) with a general loss function and unknown parameters. To mitigate the epistemic uncertainty associated with unknown parameters, we take a Bayesian approach…

Neural ODE Processes approach the problem of meta-learning for dynamics using a latent variable model, which permits a flexible aggregation of contextual information. This flexibility is inherited from the Neural Process framework and…

Both experimental and computational methods for the exploration of structure, functionality, and properties of materials often necessitate the search across broad parameter spaces to discover optimal experimental conditions and regions of…

Predictive dynamical models for marine ecosystems are used for a variety of needs. Due to sparse measurements and limited understanding of the myriad of ocean processes, there is however significant uncertainty. There is model uncertainty…