An Introduction to Empirical Bayes Data Analysis

Bayes and Empirical Bayes Methods for Data Analysis

Introduction to circular data

In many diverse scientific fields, the measurements are directions. For instance, a biologist may be measuring the direction of flight of a bird or the orientation of an animal. A series of such observations is called ”directional data”. Since a direction has no magnitude, these can be conveniently represented as points on the circumference of a unit circle centered at the origin or as unit ...

Data envelopment analysis in service quality evaluation: an empirical study

Service quality is often conceptualized as the comparison between service expectations and the actual performance perceptions. It enhances customer satisfaction, decreases customer defection, and promotes customer loyalty. Substantial literature has examined the concept of service quality, its dimensions, and measurement methods. We introduce the perceived service quality index (PSQI) as a sing...

An Improved Bayes Empirical Bayes Estimator

Consider an experiment yielding an observable random quantity X whose distribution Fθ depends on a parameter θ with θ being distributed according to some distribution G0. We study the Bayesian estimation problem of θ under squared error loss function based on X, as well as some additional data available from other similar experiments according to an empirical Bayes structure. In a recent paper,...

An Empirical Bayes Approach to Statistics

Let X be a random variable which for simplicity we shall assume to have discrete values x and which has a probability distribution depending in a known way on an unknown real parameter A, (1) p (xIX) =Pr [X = xIA =X], A-itself being a random variable with a priori distribution function (2) G (X) =Pr [A-< X. The unconditional probability distribution of X is then given by (3) PG(x) =Pr[X=xI =fP(...