Some Thoughts on Empirical Bayes Estimation

Empirical Bayes Estimation in Nonstationary Markov chains

Estimation procedures for nonstationary Markov chains appear to be relatively sparse. This work introduces empirical  Bayes estimators  for the transition probability  matrix of a finite nonstationary  Markov chain. The data are assumed to be of  a panel study type in which each data set consists of a sequence of observations on N>=2 independent and identically dis...

Some Thoughts on Replication in Empirical Econometrics

Empirical Bayes Estimation of Reliability

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...

Empirical Bayes and Full Bayes for Signal Estimation

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...

Two modeling strategies for empirical Bayes estimation.

Empirical Bayes methods use the data from parallel experiments, for instance observations Xk ~ 𝒩 (Θ k , 1) for k = 1, 2, …, N, to estimate the conditional distributions Θ k |Xk . There are two main estimation strategies: modeling on the θ space, called "g-modeling" here, and modeling on the×space, called "f-modeling." The two approaches are de- scribed and compared. A series of computational fo...