相关论文: On the behavior of Bayesian credible intervals for…
Selecting appropriate regularization coefficients is critical to performance with respect to regularized empirical risk minimization problems. Existing theoretical approaches attempt to determine the coefficients in order for regularized…
Consider the problem of estimating a multivariate normal mean with a known variance matrix, which is not necessarily proportional to the identity matrix. The coordinates are shrunk directly in proportion to their variances in Efron and…
This paper makes two contributions towards determining some well-studied optimal constants in Fourier analysis \newa{of Boolean functions} and high-dimensional geometry. \begin{enumerate} \item It has been known since 1994 \cite{GL:94} that…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
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…
The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power…
We consider the problem of inference for projection parameters in linear regression with increasing dimensions. This problem has been studied under a variety of assumptions in the literature. The classical asymptotic normality result for…
We consider the problem of heteroscedastic linear regression, where, given $n$ samples $(\mathbf{x}_i, y_i)$ from $y_i = \langle \mathbf{w}^{*}, \mathbf{x}_i \rangle + \epsilon_i \cdot \langle \mathbf{f}^{*}, \mathbf{x}_i \rangle$ with…
In wavelet shrinkage and thresholding, most of the standard techniques do not consider information that wavelet coefficients might be bounded, although information about bounded energy in signals can be readily available. To address this,…
In this paper, we derive closed-form exact expressions for the main statistics of the ratio of squared alpha-mu random variables, which are of interest in many scenarios for future wireless networks where generalized distributions are more…
We present a distribution optimization framework that significantly improves confidence bounds for various risk measures compared to previous methods. Our framework encompasses popular risk measures such as the entropic risk measure,…
We propose a novel spike and slab prior specification with scaled beta prime marginals for the importance parameters of regression coefficients to allow for general effect selection within the class of structured additive distributional…
The upper bounds on the coverage probabilities of the confidence regions based on blockwise empirical likelihood [Kitamura (1997)] and nonstandard expansive empirical likelihood [Nordman et al. (2013)] methods for time series data are…
Models of weak-scale supersymmetry offer viable dark matter (DM) candidates. Their parameter spaces are however rather large and complex, such that pinning down the actual parameter values from experimental data can depend strongly on the…
The implementation of Bayesian predictive procedures under standard normal models is considered. Two distributions are of particular interest, the K-prime and K-square distributions. They also give exact inferences for simple and multiple…
Random effects model can account for the lack of fitting a regression model and increase precision of estimating area-level means. However, in case that the synthetic mean provides accurate estimates, the prior distribution may inflate an…
For normal canonical models, and more generally a vast array of general spherically symmetric location-scale models with a residual vector, we consider estimating the (univariate) location parameter when it is lower bounded. We provide…
Adaptivity is an important feature of data analysis---typically the choice of questions asked about a dataset depends on previous interactions with the same dataset. However, generalization error is typically bounded in a non-adaptive…
We identify the critical deviation scale governing Bayesian evidence accumulation in regular parametric testing. Under integrated Bayes risk with zero-one loss, the risk-optimal rejection boundary lies in a moderate deviation regime, with a…
The prominent Bernstein -- von Mises (BvM) result claims that the posterior distribution after centering by the efficient estimator and standardizing by the square root of the total Fisher information is nearly standard normal. In…