Authorship

###### 1. Roy Felton

Business Computing and Economics Department - Manukau Institute of Technology

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The Bayesian approach of Mosteller and Wallace1

to the question of the authorship of the Federalist

Papers can be applied to the situation of disputed

writing(s) being assigned to one or other of a

limited number of known authors, each of whom

has a known style. Another quite distinct situation

frequently occurs in the case of classical and other

ancient writings. Here there is often an undisputed

corpus of texts (by a known or unknown author or

group of authors) with another text or texts (hereafter treated in the singular only), which has been

traditionally linked to this body but its authorship

has been disputed on critical grounds. The problem is to determine whether this disputed text is

close enough in style to that of the undisputed texts

in order for it to belong to this group and hence

presumably have the same author or group of

authors. (Whether the corpus itself exhibits a unity

of style between texts as well as the more usual

assumption of unity of style within each text is

unimportant.)

This problem can be handled by using contrasts on

a random effects linear model. Either means or

proportions (binary variables) can be used. The

technique has a multivariate variant. The linear

model may be generalised to include any number

of factors such as text, genre and subject matter

effects. Factors could be fixed or random, crossed

or nested. Text is to be regarded as a random effect,

but genre and subject matter as fixed. Genre and

subject matter could be crossed or perhaps nested,

whereas text and genre would be nested. At least

two texts of undisputed provenance (not necessarily of the same length) are required. Usually

contrasts (a linear combination of means with a

zero sum for the coefficients of the means) are

used with a fixed effects model to test hypotheses.

However, in the above situation with ancient writings, the number of potential texts by an author

may be conceived of as unlimited and hence a

random effect is appropriate. Since only some

texts of this author are extant or indeed ever written, a contrast comparing only the extant ones

against the disputed one is all that a researcher

would probably be interested in. In the case of a

random effect, its associated measure of variability (which is always made to be non negative) may

be estimated from all the texts and used in the

denominator of the test statistic ensuring that a

more conservative test results. This would help to

counter the well documented fact that frequently

a stylometric test will reject an undisputed text2

By making allowance for other sources of variation as well as that due to sampling, confounding

of effects will be reduced resulting in a statistically

superior methodology. The use of contrasts on a

random effects model appears to be unique in

stylometric research and possibly elsewhere as

well.

A Bayesian type approach may be utilised to integrate out parameters, the estimates of which might

be based on too little data (usually because the

number of undisputed texts is small) to give very

precise estimates. Autocorrelation, both within

and between texts, may be incorporated into the

linear model. Critical values can be obtained by

simulation, which enables the case of discrete

variables to be catered for in a straightforward

manner as well as various types of autocorrelation.

During simulation the effect of changing blocksize (number of words of running text that each

observation is based on) but not text length was

examined, noting that power was substantially

increased when instead of 100-word blocks, 25-

word blocks were used.

Words may be examined individually also (blocksize of 1 word) giving rise to binary variables.

These may be handled in an analogous way to

count, derived or other variables. In this case it is

more appropriate to estimate the text effect variability using only the undisputed writings.

The above approach of using contrasts on a random effects model was developed to solve a simply formulated problem drawn from the Christian

Scriptures. There has been a somewhat persistent

stream of critical thought this century which has

sought to find an underlying source for a significant amount of the narrative portions of John’s

gospel. One proposal for a source for the synoptic-like miracle stories in this gospel, that has

reasonably precisely defined limits, is Fortna’s

Gospel of Signs (hereafter FGOS).3

This reconstruction of the somewhat shadowy and elusive

so-called signs source seems to enjoy a certain

amount of support and its Greek text is available

enabling a detailed statistical examination to be

carried out.

John’s gospel was divided into three equal sized

main sections, each of 30 blocks of 100 words in

each. The three sections were F (derived from

FGOS), N (derived from the narrative portions of

the gospel) and D (derived from the discourse

portions of the gospel). Each block began at the

beginning of a sentence, which for this investigation was defined as a string of words terminated

by fullstops, semicolons or question marks. Sentences that contained identifiable quotations from

the Hebrew Scriptures were omitted from the count.

Twenty-four simple-to-measure variables were

used to measure style. Variables 1-10 were the

number of words in each block of 1 letter, 2 letters

up to 10 letters long. Variable 11 was the number

of definite articles beginning with a tau. Variable

12 was the number of other words beginning with

a tau. Variable 13 was the number of definite

articles. Variable 14 was the number of indefinite

and relative pronouns. Variable 15 was the mean

word position of the first noun in a sentence (or

part sentence). Variable 16 was the number of

sentences (or part sentences). Variables 17-24

were the number of V-V, V-N, V-O, N-V, N-N,

N-O, O-V and O-N transitions where V = verb, N

= noun and O = other.

Variables 1, 3, 8, 11 and 13 were initially removed

since they were highly autocorrelated although

they were restored later when autocorrelation was

built into the model. A modification of the usual

pooled t test statistic was used to test the hypothesis whether the style of F differed significantly

from the other two making allowance for the fact

that these two themselves might differ significantly from each other. Variables 3, 7, 14, 16, and 23

were judged to be significant at the 5% level.

Because, if the N and D portions of the gospel were

written at the same time, the estimate of the variability of the text effect would in fact be measuring

that of the genre effect since the text effect would

be non existent, it was decided to include in the

study the first Johannine letter (referred to subsequently as J) which was divided into 19 blocks

of 100 words. It is almost certain J was written

later than N. Hence N and J were used to estimate

the variability of text effect which because of

confounding included genre effect also. This variability was then used in the modified t test statistic to see if F and N (both belonging to the

narrative genre) were significantly different. Since, if anything, the variability was inflated by

genre this approach would be conservative. Variables 8, 15 and probably 16 were significant at the

5% level. The estimate of the inter-text variability

was based on only two observations, meaning it

would not be very precise. Since the critical value

for the test statistic was a function of its true value

it was decided to integrate this parameter out

which resulted in no change in variables that were

judged to be significant. However when further

the test statistic was conditioned on its observed

value, variable 8 and probably 10 were now significant at the 5% level.

Variables 1-14 and 17-24 may also be regarded as

binary - that is each word for variables 1-14 or pair

of words for variables 17-24 may be coded as 1 or

0 depending on whether the particular property is

present or not. The above stages of analysis were

carried out using a binary random effects model

with very similar results.

This investigation concluded that the balance of

probability was that the style of F differed from

that of N and D and indeed J by more than could

be expected by chance even when an effort to take

genre into account was made. However the decision was not as clear cut as one might have wished.

If more undisputed texts (say 8) were available,

the result could well have been quite significant.

Also if more sophisticated (linguistically speaking) variables were utilised, a more decisive result could very well eventuate. Because a statistically significant test statistic was obtained with

some of the 24 variables chosen, under the Baconian rule of the greater force of one counter-example than that of several supporting examples, it

must be concluded that earlier, less statistically

sophisticated stylometric investigations of John’s

gospel, which demonstrated its unity, have been

superseded by this study.

Because it appears that numerous scholars champion either the unity of or some form of source

theory for John’s gospel it seems appropriate that

the results of this investigation, while consistently

supporting sources in a statistically significant

sense, do so to a measured degree only, suggesting

that New Testament scholars have not been completely misled in their more intuitive and less

statistically sophisticated evaluation of the style of

John’s gospel. This investigation does not establish whether all the signs source was reproduced

in the gospel or not or indeed whether that part

which was, has been done so in a faithful manner.

What has been demonstrated is that Fortna’s reconstruction has a style sufficiently different from

other narrative in the gospel to suggest a different

origin.

References

1. Mosteller, F. and D. L. Wallace. Inference and

Disputed Authorship: The Federalist. Reading, Massachusetts: Addison-Wesley, 1964.

2. Felton, T. R. Stylometry - An Example. Conference Proceedings. Operations Research Society of New Zealand / New Zealand

Statistical Association Annual Conference

(1994): 350-3.

3. Fortna, R. T. The Gospel of Signs: A Reconstruction of the Narrative Source Underlying

the Fourth Gospel. Cambridge: Cambridge

University Press, 1970.

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Conference Info

In review

Hosted at University of Bergen

Bergen, Norway

June 25, 1996 - June 29, 1996

147 works by 190 authors indexed

Scott Weingart has print abstract book that needs to be scanned; certain abstracts also available on dh-abstracts github page. (https://github.com/ADHO/dh-abstracts/tree/master/data)

Conference website: https://web.archive.org/web/19990224202037/www.hd.uib.no/allc-ach96.html

Tags

**Keywords:**binary contrasts stylometry**Language:**English**Topics:**None