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We study the self-normalized concentration of vector-valued stochastic processes. We focus on bounds for "sub-$\psi$" processes, a well-known and quite general class of process that encompasses a wide variety of well-known tail conditions…

Two of the principle tasks of causal inference are to define and estimate the effect of a treatment on an outcome of interest. Formally, such treatment effects are defined as a possibly functional summary of the data generating…

We propose a class of transformation hazard models for right-censored failure time data. It includes the proportional hazards model (Cox) and the additive hazards model (Lin and Ying) as special cases. Due to the requirement of a…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

We present a quasi-conjugate Bayes approach for estimating Generalized Pareto Distribution (GPD) parameters, distribution tails and extreme quantiles within the Peaks-Over-Threshold framework. Damsleth conjugate Bayes structure on Gamma…

Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…

Linear mixed-effects models are a central analytical tool for modeling hierarchical and longitudinal data, as they allow simultaneous representation of fixed and random sources of variation. In practice, inference for such models is most…

Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable…

This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…

There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on…

Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…

We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…

This paper builds on recent research that focuses on regression modeling of continuous bounded data, such as proportions measured on a continuous scale. Specifically, it deals with beta regression models with mixed effects from a Bayesian…

We consider a sparse linear regression model with unknown symmetric error under the high-dimensional setting. The true error distribution is assumed to belong to the locally $\beta$-H\"{o}lder class with an exponentially decreasing tail,…

The use of non parametric hidden Markov models with finite state space is flourishing in practice while few theoretical guarantees are known in this framework. Here, we study asymptotic guarantees for these models in the Bayesian framework.…

Univariate and multivariate general linear regression models, subject to linear inequality constraints, arise in many scientific applications. The linear inequality restrictions on model parameters are often available from phenomenological…

Bayesian methods are a popular choice for statistical inference in small-data regimes due to the regularization effect induced by the prior. In the context of density estimation, the standard nonparametric Bayesian approach is to target the…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

Power posteriors "robustify" standard Bayesian inference by raising the likelihood to a constant fractional power, effectively downweighting its influence in the calculation of the posterior. Power posteriors have been shown to be more…

Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…