1. Hui Ping, Chuan Yin, Xuan Qi Group 5
FMS1204S Week 9 HAMILTON OR MADISON? WHO WROTE THE DISPUTED FEDERALIST PAPERS? (MOSTELLER, 2010)
Hui Ping, Chuan Yin, Xuan Qi
Group 5

2. Frederick Mosteller (1916-2006)
Statistics pioneer – including use of statistics in authorship studies

3. Points of discussion
The history of Mosteller’s studies of authorship of the Federalist papers
Methods Mosteller and his collaborators tried
Method that was most crucial – Bayesian statistics

4. Federalist papers (1787-1788) Alexander Hamilton James Maddison
To persuade citizens of New York to ratify the Constitution
(formally consent to and validate it)
Important to study of political philosophy
12 works disputed, 3 of joint authorship to debated extent

5. prelude G. Udny Yule - distribution of sentence length
Kempis was author of Imitatio, since the work’s distribution fits that of his other works
C.B. Williams – shape of distribution of log(sentence length)

6. In a time of early computers
Cut out slips with one word on them and collate
Albert Beaton asked to write a concordance program (alphabetize and count usage) so that they could use computer to analyse
Took months to program and it was glitchy if used for long

7. Early years (1941) – with fred williams
Method: sentence length (by word count)
Results:
Average length vs 34.59
Standard deviation -19 vs 20
FAILURE

8. Method: noun-adjective ratio
Results:
Hard to classify as either (e.g. “own”)
Differences between Hamilton and Maddison were again too small
FAILURE

9. Method: Fisher’s discriminant function
To differentiate between two objects/events
<one- and two-letter words> and <number of “the”s>
Results:
Discriminant obtained for each paper too small for confident conclusion
If they were all added up (which answers who wrote the disputed papers as a whole) – it would point to Maddison
FAILURE

10. Fisher’s discriminant
Recap – early methods
Fail!
Sentence length
Noun-adjective ratio
Fisher’s discriminant

11. 1955 – working with david wallace
Method: Bayesian inference
Wikipedia definition – “Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available.”
System for dealing with uncertainty and use of new info
Get more accurate probability
Final results in terms of odds

12. Adair’s suggestion for Bayesian method
Give different weightage to different word types
Those that vary a lot due to topic change – low weight
Those that vary little – higher weight
Eg conjunctions, prepositions, articles, adverbs, abstract nouns
rate of use more author-dependent than topic- dependent

13. Maddison uses “by” more often than Hamilton
Paper with higher rate of “by”  Maddison
Cross reference with all the other markers

14. The more distinct each author’s distribution is from the other, the better power to discriminate
by > to > from

15. Bayesian inference – markers
Marker words – only one author uses
These do not appear often though – use enough of them and add up
Not fully certain the other author will never use the word
May slip up and use it
While – Hamilton ; Whilst – Maddison
Maddison slipped and used “while” twice in other writings

16. Making inferences despite having uncertainties
Use rate or relative frequency of marker use
Not “was marker used?” - yes means X, no means Y wrote it
Some words were used often by one and rarely by the other
Upon, Enough – Hamilton > Maddison

17. Constructing probability model
To represent word rate difference between the papers
Simplest model – the urn
From drawing at random a coloured ball, determining probability of drawing this colour and that

18. Building on urn model
Negative binomial distribution used to account for when some papers had slightly different rates than their usual pattern
In “urn model” terms, it is how many times you get correct colour before you get the incorrect one for a specified number of times
Using negative binomial model gave odds of 100 to 1, but if simple urn model was used it would be 10,000 to 1 (100^2)
Which would be highly misleading
So the shape of data distribution was very important

19. Bayesian inference data Topic-independent words Marker words analysis
Probability model
Negative binomial distribution

20. results All methods support Madison as the author
Even “weakest” odds for Paper 55 were 80 to 1 for Maddison
Next “weakest” was for Paper to 1
These are both both already strong and very strong odds

21. conclusion
Mosteller-Wallace approach was among the pioneering large- scale use of Bayesian method
Made possible by the arrival of early modern computers
Example of text data-mining (“bag of words”)
Due to Mosteller’s influence, nowadays the method to determine authorship is with high-frequency function words.