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The goal of this presentation is to build an efficient non-parametric Bayes classifier in the presence of large numbers of predictors. When analyzing such data, parametric models are often too inflexible while non-parametric procedures tend…

This work develops rigorous theoretical basis for the fact that deep Bayesian neural network (BNN) is an effective tool for high-dimensional variable selection with rigorous uncertainty quantification. We develop new Bayesian non-parametric…

We investigate the asymptotic properties of Bayesian bivariate causal discovery for Gaussian Linear Structural Equation Models (SEMs) with heteroscedastic noise. We demonstrate that with purely observational data, the posterior distribution…

We investigate the asymptotic normality of the posterior distribution in the discrete setting, when model dimension increases with sample size. We consider a probability mass function $\theta_0$ on $\mathbbm{N}\setminus \{0\}$ and a…

Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of…

We investigate the frequentist posterior contraction rate of nonparametric Bayesian procedures in linear inverse problems in both the mildly and severely ill-posed cases. A theorem is proved in a general Hilbert space setting under…

This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis…

Many inverse problems arising in applications come from continuum models where the unknown parameter is a field. In practice the unknown field is discretized resulting in a problem in $\mathbb{R}^N$, with an understanding that refining the…

Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…

The formalism of quantum estimation theory with a specific focus on classical data postprocessing is applied to a two-level system driven by an external gyrating magnetic field. We employed both Bayesian and frequentist approaches to…

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…

In the paper, we present a strategy for accelerating posterior inference for unknown inputs in time fractional diffusion models. In many inference problems, the posterior may be concentrated in a small portion of the entire prior support.…

This paper is concerned with the estimation of the period of an unknown periodic function in Gaussian white noise. A class of estimators of the period is constructed by means of a penalized maximum likelihood method. A second-order…

As Basu (1977) writes, "Eliminating nuisance parameters from a model is universally recognized as a major problem of statistics," but after more than 50 years since Basu wrote these words, the two mainstream schools of thought in statistics…

The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

Bayesian inversion generates a posterior distribution of model parameters from an observation equation and prior information both weighted by hyperparameters. The prior is also introduced for the hyperparameters in fully Bayesian inversions…

Bayesian online learning provides a coherent framework for sequential inference. However, its theoretical understanding remains limited, particularly in the one-pass setting. Existing theoretical guarantees typically require the mini-batch…

We study large sample properties of Bayesian analysis of the proportional hazard model with neutral to the right process priors on the baseline hazard function. We show that the posterior distribution of the baseline cumulative hazard…

In this paper, we study the learning rate of generalized Bayes estimators in a general setting where the hypothesis class can be uncountable and have an irregular shape, the loss function can have heavy tails, and the optimal hypothesis may…