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We undertake Bayesian learning of the high-dimensional functional relationship between a system parameter vector and an observable, that is in general tensor-valued. The ultimate aim is Bayesian inverse prediction of the system parameters,…
Stochastic Differential Equations (SDEs) are used as statistical models in many disciplines. However, intractable likelihood functions for SDEs make inference challenging, and we need to resort to simulation-based techniques to estimate and…
This paper studies the covariance matrix estimation for high-dimensional time series within a new framework that combines low-rank factor and latent variable-specific cluster structures. The popular methods based on assuming the sparse…
This paper addresses the adaptive radar target detection problem in the presence of Gaussian interference with unknown statistical properties. To this end, the problem is first formulated as a binary hypothesis test, and then we derive a…
This paper considers multiple regression procedures for analyzing the relationship between a response variable and a vector of covariates in a nonparametric setting where both tuning parameters and the number of covariates need to be…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
Nonlinear Mixed effects models are hidden variables models that are widely used in many fields such as pharmacometrics. In such models, the distribution characteristics of hidden variables can be specified by including several parameters…
Maximizing the likelihood has been widely used for estimating the unknown covariance parameters of spatial Gaussian processes. However, evaluating and optimizing the likelihood function can be computationally intractable, particularly for…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
Common workflows in machine learning and statistics rely on the ability to partition the information in a data set into independent portions. Recent work has shown that this may be possible even when conventional sample splitting is not…
We study the problem of estimating the covariance parameters of a one-dimensional Gaussian process with exponential covariance function under fixed-domain asymptotics. We show that the weighted pairwise maximum likelihood estimator of the…
Anomaly detection is a field of intense research. Identifying low probability events in data/images is a challenging problem given the high-dimensionality of the data, especially when no (or little) information about the anomaly is…
We propose a flexible Bayesian approach for estimating the joint density of a multivariate outcome of interest in the presence of categorical covariates. Leveraging a Gaussian copula framework, our method effectively captures the dependence…
Gaussian processes (GPs) are Bayesian non-parametric models popular in a variety of applications due to their accuracy and native uncertainty quantification (UQ). Tuning GP hyperparameters is critical to ensure the validity of prediction…
For predictive modeling relying on Bayesian inversion, fully independent, or ``mean-field'', Gaussian distributions are often used as approximate probability density functions in variational inference since the number of variational…
Datasets containing both categorical and continuous variables are frequently encountered in many areas, and with the rapid development of modern measurement technologies, the dimensions of these variables can be very high. Despite the…
Pairwise likelihood is a useful approximation to the full likelihood function for covariance estimation in high-dimensional context. It simplifies high-dimensional dependencies by combining marginal bivariate likelihood objects, thus making…
In regression models for spatial data, it is often assumed that the marginal effects of covariates on the response are constant over space. In practice, this assumption might often be questionable. In this article, we show how a Gaussian…
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 consider generalized linear regression analysis with left-censored covariate due to the lower limit of detection. Complete case analysis by eliminating observations with values below limit of detection yields valid estimates for…