Related papers: Posterior Consistency in the Binomial $(n,p)$ Mode…
We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance parameters can be finite-, high-, or infinite-dimensional. A mixture…
We consider a family of infinite dimensional product measures with tails between Gaussian and exponential, which we call $p$-exponential measures. We study their measure-theoretic properties and in particular their concentration. Our…
It is well known that a binomial $(n,p)$ can be approximated by a Poisson distribution with parameter $np$. The typical approach in undergraduate probability texts is to show a convergence result for the distribution of the binomial as $n$…
Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…
The exact expression is derived for the expected value, $< {p_i}> $, for the parameter for any bin $i$ of a histogram following a multinomial distribution derived by sorting $N$ observations into bins of $B$ classes, if $n_i$ of the…
We study Bayesian inference of an unknown matching $\pi^*$ between two correlated random point sets $\{X_i\}_{i=1}^n$ and $\{Y_i\}_{i=1}^n$ in $[0,1]^d$, under a critical scaling $\|X_i-Y_{\pi^*(i)}\|_2 \asymp n^{-1/d}$, in both an exact…
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…
Posterior sampling with the spike-and-slab prior [MB88], a popular multimodal distribution used to model uncertainty in variable selection, is considered the theoretical gold standard method for Bayesian sparse linear regression [CPS09,…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
The Bernstein-von Mises theorem (BvM) gives conditions under which the posterior distribution of a parameter $\theta\in\Theta\subseteq\mathbb R^d$ based on $n$ independent samples is asymptotically normal. In the high-dimensional regime, a…
We examine the Bayes-consistency of a recently proposed 1-nearest-neighbor-based multiclass learning algorithm. This algorithm is derived from sample compression bounds and enjoys the statistical advantages of tight, fully empirical…
In this paper, we consider Bayesian point estimation and predictive density estimation in the binomial case. After presenting preliminary results on these problems, we compare the risk functions of the Bayes estimators based on the…
The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…
We present a procedure for calculating an upper limit on the number of signal events which incorporates the Poisson uncertainty in the background, estimated from control regions of one or two dimensions. For small number of signal events,…
Consider the observation of n iid realizations of an experiment with d>1 possible outcomes, which corresponds to a single observation of a multinomial distribution M(n,p) where p is an unknown discrete distribution on {1,...,d}. In many…
Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…
The "large p, small n" paradigm arises in microarray studies, where expression levels of thousands of genes are monitored for a small number of subjects. There has been an increasing demand for study of asymptotics for the various…
Posterior computation for high-dimensional data with many parameters can be challenging. This article focuses on a new method for approximating posterior distributions of a low- to moderate-dimensional parameter in the presence of a…
Parameter estimation and inference from complex survey samples typically focuses on global model parameters whose estimators have asymptotic properties, such as from fixed effects regression models. The central challenge is to both mitigate…
Let $\{Z_t, t\geq 0\}$ be a strictly stable process on $\R$ with index $\alpha\in (0,2]$. We prove that for every $p > \alpha$, there exists $\gamma = \gamma (\alpha, p)$ and $\k = \k (\alpha, p)\in (0, +\infty)$ such that…