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We consider uniform moment convergence of lag-window spectral density estimates for univariate and multivariate stationary processes. Optimal rates of convergence are obtained under mild and easily verifiable conditions. Our theory…

Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…

We develop a new approach for quantifying uncertainty in finite populations, by using design distributions to calibrate sensitivity parameters in finite population identified sets. This yields uncertainty intervals that can be interpreted…

Accurate uncertainty estimates are important in sequential model-based decision-making tasks such as Bayesian optimization. However, these estimates can be imperfect if the data violates assumptions made by the model (e.g., Gaussianity).…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…

Incentives in experimental design are often misaligned: experimenters design and finance experiments to seek regulatory approval, while regulators seek to maximize social-welfare. We propose a framework to resolve this conflict, wherein…

We provide sufficient conditions under which a utility function may be recovered from a finite choice experiment. Identification, as is commonly understood in decision theory, is not enough. We provide a general recoverability result that…

We establish novel quantitative stability results for optimal transport problems with respect to perturbations in the target measure. We provide explicit bounds on the stability of optimal transport potentials and maps, which are relevant…

We develop a computational framework for D-optimal experimental design for PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We follow a formulation of the experimental design problem that remains valid in the…

Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…

This paper is concerned with Bayesian inferential methods for data from controlled branching processes that account for model robustness through the use of disparities. Under regularity conditions, we establish that estimators built on…

We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…

We consider optimal experimental design (OED) for nonlinear inverse problems within the Bayesian framework. Optimizing the data acquisition process for large-scale nonlinear Bayesian inverse problems is a computationally challenging task…

Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…

History-dependent constitutive models serve as macroscopic closures for the aggregated effects of micromechanics. Their parameters are typically learned from experimental data. With a limited experimental budget, eliciting the full range of…

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…

This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…

In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or…

We establish local existence and a quasi-optimal error estimate for piecewise cubic minimizers to the bending energy under a discretized inextensibility constraint. In previous research a discretization is used where the inextensibility…

We present an efficient method for computing A-optimal experimental designs for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we address the problem of optimizing the…