Name: Inference and Disputed Authorship
Author: Nerbonne, John
ISBN: 9780387909912

Inference and Disputed Authorship

by Frederick Mosteller and David L. Wallace
introduction by John Nerbonne

CSLI, 2013
Cloth: 978-0-387-90991-2 | Paper: 978-1-57586-552-2 | eISBN: 978-1-57586-718-2
Library of Congress Classification JK155.M59 2007
Dewey Decimal Classification 342.73029

ABOUT THIS BOOK | AUTHOR BIOGRAPHY | TOC

ABOUT THIS BOOK

The 1964 publication of Inference and Disputed Authorship made the cover of Time magazine and the attention of academics and the public alike for its use of statistical methodology to solve one of American history’s most notorious questions: the disputed authorship of the Federalist Papers.

Back in print for a new generation of readers, this classic volume applies mathematics, including the once-controversial Bayesian analysis, into the heart of a literary and historical problem by studying frequently used words in the texts. The reissue of this landmark book will be welcomed by anyone interested in the juncture of history, political science, and authorship.

AUTHOR BIOGRAPHY

Frederick Mosteller (1916–2006) was professor of statistics at Harvard University.
David L. Wallace is professor emeritus of statistics at the University of Chicago.

TABLE OF CONTENTS

Analytic Table of Contents

Chapter 1.
The Federalist Papers As a Case Study

1.1.
Purpose

1.2.
The Federalist papers

1.3.
Early work

1.4.
Recent work—pilot study

1.5.
Plots and honesty

1.6.
The plan of the book

Chapter 2.
Words and Their Distributions

2.1.
Why words?

2.2.
Variation with time

2.3.
How frequency of use varies

2.3A.
Independence of words from one block of text to another

2.3B.
Frequency of occurrence

2.4.
Correlations between rates for different words

2.5.
Pools of words

2.5A.
The function words

2.5B.
Initial screening study

2.5C.
Word index with frequencies

2.6.
Word counts and their accuracies

2.7.
Concluding remarks

Chapter 3.
The Main Study

3.1.
Introduction to Bayes' theorem and its applications

3.1A.
An example applying Bayes' theorem with both initial odds and parameters known

3.1B.
Selecting words and weighting their evidence

3.1C.
Initial odds

3.1D.
Unknown parameters

3.2.
Handling unknown parameters of data distributions

3.2A.
Choosing prior distributions

3.2B.
The interpretation of the prior distributions

3.2C.
Effect of varying the prior

3.2D.
The posterior distribution of (σ, τ)

3.2E.
Negative binomial

3.2F.
Final choices of underlying constants

3.3.
Selection of words

3.4.
Log odds

3.4A.
Checking the method

3.4B.
The disputed papers

3.5.
Log odds by words and word groups

3.5A.
Word groups

3.5B.
Single words

3.5C.
Contributions of marker and high-frequency words

3.6.
Late Hamilton papers

3.7.
Adjustments to the log odds

3.7A.
Correlation

3.7B.
Effects of varying the underlying constants that determine the prior distributions

3.7C.
Accuracy of the approximate log odds calculation

3.7D.
Changes in word counts

3.7E.
Approximate adjusted log odds for the disputed papers

3.7F.
Can the odds be believed?

Chapter 4.
Theoretical Basis of the Main Study

4.1.
The negative binomial distribution

4.1A.
Standard properties

4.1B.
Distributions of word frequency

4.1C.
Parametrization

4.1D.
Estimation

4.2.
Analysis of the papers of known authorship

4.2A.
The data: notations and distributional assumptions

4.2B.
Object of the analysis

4.2C.
Prior distributions: assumptions

4.2D.
The posterior distribution

4.2E.
The modal estimates

4.2F.
An alternative choice of modes

4.2G.
Choice of initial estimate

4.3.
Abstract structure of the main study

4.3A.
Notation and assumptions

4.3B.
Stages of analysis

4.3C.
Derivation of the odds formula

4.3D.
Historical information

4.3E.
Odds for single papers

4.3F.
Prior distributions for many nuisance parameters

4.3G.
Summary

4.4.
Odds factors for the negative binomial model

4.4A.
Odds factors for an unknown paper

4.4B.
Integration difficulties in evaluation of λ

4.4C.
Behavior of likelihood ratios

4.4D.
Summary

4.5.
Choosing the prior distributions

4.5A.
Estimation of β1 and β2: first analysis

4.5B.
Estimation of β1 and β2: second analysis

4.5C.
Estimation of β3

4.5D.
Estimation of β4 and β5

4.5E.
Effect of varying the set of underlying constants

4.5F.
Upon: a case study

4.5G.
Summary

4.6.
Magnitudes of adjustments required by the modal approximation to the odds factor

4.6A.
Ways of studying the approximation

4.6B.
Normal theory for adjusting the negative binomial modal approximation

4.6C.
Approximations to expectations

4.6D.
Notes on asymptotic methods

4.7.
Correlations

4.7A.
Independence and odds

4.7B.
Adjustment for a pair of words

4.7C.
Example. The words upon and on

4.7D.
Study of 15 word pairs

4.7E.
Several words

4.7F.
Further theory

4.7G.
Summary

4.8.
Studies of regression effects

4.8A.
Introduction

4.8B.
The study of word rates

4.8C.
Total log odds for the final 30 words

4.8D.
Log odds by word group

4.8E.
Theory for the Poisson model

4.8F.
Theory for the negative binomial model

4.8G.
Two-point formulas for expectations of negative binomial log odds

4.9.
A logarithmic penalty study

4.9A.
Probability predictions

4.9B.
The Federalist application: procedure

4.9C.
The Federalist application: the penalty function

4.9D.
The Federalist application: numerical results

4.9E.
The Federalist application: adjusted log odds

4.9F.
The choice of penalty function

4.9G.
An approximate likelihood interpretation

4.10.
Techniques in the final choice of words

4.10A.
Systematic variation in Madison's writing

4.10B.
Theory

Chapter 5.
Weight-Rate Analysis

5.1.
The study, its strengths and weaknesses

5.2.
Materials and techniques

5.3.
Results for the screening and calibrating sets

5.4.
Regression effects

5.5.
Results for the disputed papers

Chapter 6.
A Robust Hand-Calculated Bayesian Analysis

6.1.
Why a robust study?

6.2.
Papers and words

6.3.
Log odds for high-frequency words

6.4.
Low-frequency words

6.5.
The procedure for low-frequency words

6.6.
Bayesian discussion for low-frequency words

6.7.
Log odds for 2000-word set and validating set

6.8.
Disputed papers

Chapter 7.
Three-Category Analysis

7.1.
The general plan

7.2.
Details of method

7.3.
Groups of words

7.4.
Results for the screening and calibrating sets

7.5.
Regression effects

7.5A.
Word group

7.5B.
The regression effect by single words

7.6.
Results for the joint and disputed papers

Chapter 8.
Other Studies

8.1.
How word rates vary from one text to another

8.2.
Making simplified studies of authorship

8.3.
The Caesar letters

8.4.
Further analysis of Paper No. 20

8.5.
How words are used

8.6.
Scattered investigations

8.7.
Distributions of word-length

Chapter 9.
Summary of Results and Conclusions

9.1.
Results on the authorship of the disputed Federalist papers

9.2.
Authorship problems

9.3.
Discrimination problems

9.4.
Remarks on Bayesian studies

9.5.
Summing up

Chapter 10.
The State of Statistical Authorship Studies in 1984

10.1.
Scope

10.2.
Computers, concordances, texts, and monographs

10.3.
General empirical work

10.4.
Poetry versus prose

10.5.
Authorship studies similar to the Junius or Federalist studies

10.5A.
And Quiet Flows the Don

10.5B.
Kesari

10.5C.
Die Nachtwachen

10.5D.
Economic history

10.6.
Homogeneity problems

10.6A.
Aristotle and Ethics

10.6B.
The Bible

10.7.
Anonymous translation

10.8.
Forensic disputes

10.8A.
Morton

10.8B.
Bailey

10.8C.
Howland will

10.9.
Concluding remarks

Appendix

References

Index

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