Question

It is agreed that Hamilton wrote 51 Federalist papers and Madison wrote 14 Federalist papers. However, there’s a dispute over how to attribute 12 other papers between these two authors. In Hamilton’s 51 papers, the word “upon” was used 3.24 times per 1000 words. In Madison’s 14 papers, the word “upon” was used 0.23 times per 1000 words.

a.) Based on the sample proportion of papers with known authorship, 51/(14+51) is a reasonable prior probability for a disputed paper to be attributed to Hamilton. Give a situation where this prior should be used over the prior that gives equal probability to both authors, and give another situation where the equal probability prior is referred.

b.) If the word “upon” is used 3 times in a disputed text of length 1,000 words and we assume the equal probability prior, what is the posterior probability the paper was written by Hamilton?

c.) Give one assumption you are making in part b that is likely unreasonable.

d.) In part b, if we change the number of “upon”s from 3 to 1, does the posterior probability increase, decrease, or stay the same?

e.) In part b, if we change the number of “upon”s to 30 and the text length to 10,000 words, does the posterior probability increase, decrease, or stay the same?

Answer 1