This document provides a review of the Dirichlet process originally given in the author’s preliminary exam paper and is presented here as a tutorial. No motivation is given (in what I’ve excerpted here), and this document is intended to be a mathematical tutorial that is still accessible to the engineer. I. THE DIRICHLET DISTRIBUTION Consider the finite, D-dimensional vector, π, having the prop...

We consider immediate predictive inference, where a subject, using a number of observations of a finite number of exchangeable random variables, is asked to coherently model his beliefs about the next observation, in terms of a predictive lower prevision. We study when such predictive lower previsions are representation insensitive, meaning that they are essentially independent of the choice of...

Web data often manifest high levels of uncertainty. We focus on categorical Web data and we represent these uncertainty levels as first or second order uncertainty. By means of concrete examples, we show how to quantify and handle these uncertainties using the BetaBinomial and the Dirichlet-Multinomial models, as well as how take into account possibly unseen categories in our samples by using t...

This course is an introduction to the mainstay of quantitative empirical work in political science, the linear regression model. We begin by putting the regression model in context by discussing causation, generalization, and quasi-experimentation. We then introduce the basic two-variable regression model, discuss its assumptions, and learn how to test hypotheses with it. This is followed by th...

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The high utilization level of emergency departments in hospitals across the United States has resulted in the serious and persistent problem of ambulance diversion. This problem is magnified by the cascading effect it has on neighboring hospitals, delays in emergency care, and the potential for patients’ clinical deterioration. We provide a predictive tool that would give advance warning to hos...

One of the most difficult challenges faced by non-native speakers of English is mastering the system of English articles. We trained a maximum entropy classifier to select among a/an, the, or zero article for noun phrases, based on a set of features extracted from the local context of each. When the classifier was trained on 6 million noun phrases, its performance was correct about 88% of the t...

A variety of mathematical forms have been developed to characterize demand functions which depend on a firm’s operational and marketing activities. Such demand functions are being increasingly used by researchers in economics and different functional areas of business. We provide a comprehensive survey of commonly-used demand models which depend on (i) price, (ii) rebate, (iii) leadtime, (iv) s...