Assessment of the reliability of various types of equipment relies on statistical inference about characteristics of reliability such as reliability function, mean lifetime of the devices, or failure rate. General techniques of statistical inference (estimation and hypotheses testing) are reviewed in Estimation; Least-Squares Estimation; Maximum Likelihood; Nonparametric Tests; Hypothesis Testi...

In data science and machine learning, hierarchical parametric models, such as mixture models, are often used. They contain two kinds of variables: observable variables, which represent the parts of the data that can be directly measured, and latent variables, which represent the underlying processes that generate the data. Although there has been an increase in research on the estimation accura...

We consider signals that follow a parametric distribution where the parameter values are unknown. To estimate such signals from noisy measurements in scalar channels, we study the empirical performance of an empirical Bayes (EB) approach and a full Bayes (FB) approach. We then apply EB and FB to solve compressed sensing (CS) signal estimation problems by successively denoising a scalar Gaussian...

In this paper, Bayesian and E – Bayesian method of estimation are proposed for estimating the parameter of Rayleigh distribution. The Bayes estimate of the parameter is derived under the assumption that the prior distribution is informative i.e. gamma prior using Linex loss function. Further, comparison between the E-Bayes estimators with the associated Bayes estimators have been carried out th...

To improve the positioning accuracy and robustness of indoor positioning technology, a fingerprint positioning method is proposed based on the Kalman filter and the probability weighted Bayes algorithm. Firstly, the optimal estimation of signal strength is calculated using the prediction and correction model of Kalman filter, and then the position is estimated using the posterior probability we...

     The quadratic loss function has been used by decision-theoretic statisticians and economists for many years.  In this paper  the estimation of scale parameter under a bounded loss function, which is adequate for assessing quality and quality improvement, is considered with restriction to the principles of invariance and risk unbiasedness. An implicit form of minimum risk scale equivariant ...

EMPIRICAL BAYES ESTIMATION IN CROSS-CLASSIFIED GAUSSIAN MODELS WITH UNBALANCED DESIGN

Bayes High-Dimensional Density Estimation Using Multiscale Dictionaries by Ye Wang Department of Statistics Duke University