Related papers: Using the COBE/DMR data as a test-bed for normalit…

Gaussian processes constitute a very powerful and well-understood method for non-parametric regression and classification. In the classical framework, the training data consists of deterministic vector-valued inputs and the corresponding…

Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…

Violation of the assumptions underlying classical (Gaussian) limit theory often yields unreliable statistical inference. This paper shows that the bootstrap can detect such violations by delivering simple and powerful diagnostic tests that…

Detecting test samples drawn sufficiently far away from the training distribution statistically or adversarially is a fundamental requirement for deploying a good classifier in many real-world machine learning applications. However, deep…

We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we…

An improved estimator for the amplitude fnl of local-type non-Gaussianity from the cosmic microwave background (CMB) bispectrum is discussed. The standard estimator is constructed to be optimal in the zero-signal (i.e., Gaussian) limit.…

We test the consistency of estimates of the non-linear coupling constant f_{NL} using non-Gaussian CMB maps generated by the method described in (Liguori, Matarrese and Moscardini 2003). This procedure to obtain non-Gaussian maps differs…

This paper proposes a Bayesian method for estimating the parameters of a normal distribution when only limited summary statistics (sample mean, minimum, maximum, and sample size) are available. To estimate the parameters of a normal…

Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…

A detection of primordial non-Gaussianity could transform our understanding of the fundamental theory of inflation. The precision promised by upcoming CMB and large-scale structure surveys raises a natural question: if a detection given a…

We present a Gaussianity test of the cosmic microwave background (CMB) polarization by analyzing the statistics of unpolarized points in the sky, classified into three distinct types: saddles, comets, and beaks. This classification of…

The challenge of understanding the Universe's dynamics, particularly the Hubble tension, requires precise measurements of the Hubble constant. Building upon the existing spectral-siren method, which capitalizes on population information…

This paper discusses a couple of approaches to removing instrument gain and baseline variation from observations of the CMB anisotropy. These techniques were tested on the COBE DMR data, a balloon experiment, and by monte carlo simulations.…

Inflationary cosmologies predict Gaussian primordial fluctuations, but subsequent gravitational lensing of the CMB disturbs its Gaussianity. Knowledge of the specific signature of lensing is necessary to distinguish a lensed Gaussian sky…

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…

Gaussian graphical models, where it is assumed that the variables of interest jointly follow a multivariate normal distribution with a sparse precision matrix, have been used to study intrinsic dependence among variables, but the normality…

We propose a Bayesian shrinkage rule to estimate the wavelet coefficients in a nonparametric regression model with Gaussian errors, based on a mixture of a point mass function at zero and a symmetric, zero-centered raised cosine…

Rapidly estimating the remaining wall thickness (RWT) is paramount for the non-destructive condition assessment evaluation of large critical metallic pipelines. A robotic vehicle with embedded magnetism-based sensors has been developed to…

Unnormalized (or energy-based) models provide a flexible framework for capturing the characteristics of data with complex dependency structures. However, the application of standard Bayesian inference methods has been severely limited…

We present methods to rigorously extract parameter combinations that are constrained by data from posterior distributions. The standard approach uses linear methods that apply to Gaussian distributions. We show the limitations of the linear…