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We present a framework for generating multiple imputations for continuous data when the missing data mechanism is unknown. Imputations are generated from more than one imputation model in order to incorporate uncertainty regarding the…

Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…

Missing data and noisy observations pose significant challenges for reliably predicting events from irregularly sampled multivariate time series (longitudinal) data. Imputation methods, which are typically used for completing the data prior…

Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known (or estimable from replicate data). A generalized method of moments approach can be used to estimate model…

This paper presents two stochastic model predictive control methods for linear time-invariant systems subject to unbounded additive uncertainties. The new methods are developed by formulating the chance constraints into deterministic form,…

Several statistical models are given in the form of unnormalized densities, and calculation of the normalization constant is intractable. We propose estimation methods for such unnormalized models with missing data. The key concept is to…

We apply random matrix theory to study the impact of measurement uncertainty on dynamic mode decomposition. Specifically, when the measurements follow a normal probability density function, we show how the moments of that density propagate…

With nonignorable missing data, likelihood-based inference should be based on the joint distribution of the study variables and their missingness indicators. These joint models cannot be estimated from the data alone, thus requiring the…

In machine learning (ML) verification, the majority of procedures are non-quantitative and therefore cannot be used for verifying probabilistic models, or be applied in domains where hard guarantees are practically unachievable. The…

Existing approaches to model uncertainty typically either compare models using a quantitative model selection criterion or evaluate posterior model probabilities having set a prior. In this paper, we propose an alternative strategy which…

Prediction, where observed data is used to quantify uncertainty about a future observation, is a fundamental problem in statistics. Prediction sets with coverage probability guarantees are a common solution, but these do not provide…

Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…

Mutual information (MI) is a fundamental measure of statistical dependence between two variables, yet accurate estimation from finite data remains notoriously difficult. No estimator is universally reliable, and common approaches fail in…

Complex phenomena in engineering and the sciences are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to estimate an…

Multivariate time series data for real-world applications typically contain a significant amount of missing values. The dominant approach for classification with such missing values is to impute them heuristically with specific values…

This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…

Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations, and when estimating uncertainty in model predictions. However, methods for doing this can be…

We introduce estimation and test procedures through divergence minimiza- tion for models satisfying linear constraints with unknown parameter. These procedures extend the empirical likelihood (EL) method and share common features with…

A spatial point process can be characterized by an intensity function which predicts the number of events that occur across space. In this paper, we develop a method to infer predictive intensity intervals by learning a spatial model using…

Combining information from multiple samples is often needed in biomedical and economic studies, but the differences between these samples must be appropriately taken into account in the analysis of the combined data. We study estimation for…