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Variable selection in linear models plays a pivotal role in modern statistics. Hard-thresholding methods such as $l_0$ regularization are theoretically ideal but computationally infeasible. In this paper, we propose a new approach, called…

A new model independent method is presented for the analysis of pulsar timing data and the estimation of the spectral properties of an isotropic gravitational wave background (GWB). We show that by rephrasing the likelihood we are able to…

We describe a Bayesian framework for estimating the time-domain noise covariance of CMB observations, typically parametrized in terms of a 1/f frequency profile. This framework is based on the Gibbs sampling algorithm, which allows for…

Systems with stochastic time delay between the input and output present a number of unique challenges. Time domain noise leads to irregular alignments, obfuscates relationships and attenuates inferred coefficients. To handle these…

We review some aspects of Bayesian and frequentist interval estimation, focusing first on their relative strengths and weaknesses when used in "clean" or "textbook" contexts. We then turn attention to observational-data situations which are…

Sparse estimation of the precision matrix under high-dimensional scaling constitutes a canonical problem in statistics and machine learning. Numerous regression and likelihood based approaches, many frequentist and some Bayesian in nature…

Most data processing techniques, applied to biomedical and sociological time series, are only valid for random fluctuations that are stationary in time. Unfortunately, these data are often non stationary and the use of techniques of…

The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that…

Datasets in engineering applications are often limited and contaminated, mainly due to unavoidable measurement noise and signal distortion. Thus, using conventional data-driven approaches to build a reliable discriminative model, and…

We consider Bayesian multiple statistical classification problem in the case where the unknown source distributions are estimated from the labeled training sequences, then the estimates are used as nominal distributions in a robust…

Fundamental machine learning theory shows that different samples contribute unequally both in learning and testing processes. Contemporary studies on DNN imply that such sample difference is rooted on the distribution of intrinsic pattern…

We consider the situation where a temporal process is composed of contiguous segments with differing slopes and replicated noise-corrupted time series measurements are observed. The unknown mean of the data generating process is modelled as…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

We describe an improved statistical downscaling method for Earth science applications using multivariate Basis Graphical Lasso (BGL). We demonstrate our method using a case study of sea surface temperature (SST) projections from CMIP6 Earth…

We consider the sequential decision optimization on the periodic environment, that occurs in a wide variety of real-world applications when the data involves seasonality, such as the daily demand of drivers in ride-sharing and dynamic…

Methods utilizing instrumental variables have been a fundamental statistical approach to estimation in the presence of unmeasured confounding, usually occurring in non-randomized observational data common to fields such as economics and…

In an era of large spectroscopic surveys of stars and big data, sophisticated statistical methods become more and more important in order to infer fundamental stellar parameters such as mass and age. Bayesian techniques are powerful methods…

We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the…

In this paper, we focus on activating only a few sensors, among many available, to estimate the state of a stochastic process of interest. This problem is important in applications such as target tracking and simultaneous localization and…

The aim of our paper is to investigate the properties of the classical phase-dispersion minimization (PDM), analysis of variance (AOV), string-length (SL), and Lomb-Scargle (LS) power statistics from a statistician's perspective. We confirm…