From @MarloweFan's answer, I find that the most recent attempt to separate Marlowe and Shakespeare stylometrically is presented here:
The authors failed to separate Marlowe from Early Shakespeare, and yet wrote a conclusion that claimed that they did so. This is dishonest, as I see it.
Known Marlowe Detected As Shakespeare
Their computer program, designed to separate these authors, found the following probable authors for these plays:
- Dido: Early Shakespeare (both methods)
- Faustus: Early Shakespeare (both methods)
- Edward II: Early Shakespeare (both methods)
- Jew of Malta: Late Shakespeare/Early Shakespeare (depending on which method they used)
So that the only works of Marlowe which were not confused as Shakespeare were Tambourlain I and II, and the Massacre at Paris.
The methodology was "leave one and compare to the rest", so by separating the Tambourlaines, they leave out Tambourlaine I and compare to a corpus that includes Tambourlaine II. This is an unsafe comparison--- it is manifest that the closest match to Tambourlaine I is Tambourlaine II. If they had combined the two Tambourlaines into one text, there is no doubt in my mind it would have been misclassified as Early Shakespeare as well. So among the Marlowe works, only The Massacre at Paris is not misidentified!
This means their program failed to separate nearly all of what Marlowe work from Shakespeare, consistently across two completely different methods, and despite their obvious bias against the Marlovian hypothesis.
One of their methods is based on vocabulary, how similar the word choice is in the works. It is notable that the vocabulary of Jew of Malta matches Late Shakespeare, because nobody else matches Late Shakespeare in any way. The other method is based on function words, which are indicative of sentence structure. Both methods agreed in their misclassification of the majority of Marlowe works as belonging to Shakespeare (the two exceptions being Tambourlaine and Massacre). This is a ridiculous failure in a paper that claims to have something negative to say about Marlovian theory, considering the low failure rate with other authors (there were only a couple of other plays by other authors misclassified in this way - please read the paper).
Known Shakespeare Detected As Marlowe
Further, one of Shakespeare's known works, I Henry VI, was misclassified as Marlow in one of the methods, and classified as Shakespeare in the other. This is also notable, because the statistical biases they list explain why it is very unlikely for a work not by Marlowe to be classified as Marlowe by vocabulary (there are fewer words in Marlowe, so you find fewer matches to rare words). The biases in their method, that they explain, make it extremely significant when even a single work is misclassified as Marlowe - it means that the vocabulary in I Henry VI is essentially a dead match to that of the few Marlowe works that exist.
Other Authors: Disputed Works not ascribed to them
There were two plays not by Shakespeare/Marlowe that were not correctly identified as by their canonical authors:
- The Family of Love (Middleton), program attributed to (Johnson/Shakespeare) by (vocabulary/function-words)
- The Case is Altered (Jonson), program attributed to (Shakespeare/Chapman) by (vocabulary/function-words).
For "The Case is Altered", Jonson did not include it in his Folio, and it is of dubious authorship. To my mind, their program conclusively establishes it was not authored by Jonson, not exclusively, and not predominantly. Since their program finds a best-match within the list, one cannot say that Shakespeare or Chapman contributed to "The Case is Altered", only that it is not by Jonson.
"The Family of Love" also is of disputed authorship, it is only attributed to Middleton by academic convention. Their program's failure should conclusively demonstrate that the canonical attribution is wrong. Their program therefore did not have a single failure other than in the case of Marlowe/Shakespeare, where the failure would have (if they hadn't stupidly separated the Tambourlaines) have misidentified all but one of Marlowe's work as Shakespeare by two different methods, and misidentified I Henry VI as by Marlowe.
Estimating chance of authorship
Given that their program is dead on accurate for every single play they examined, only failing to discriminate between Shakespeare and Marlowe, one can estimate the probability that they are different authors. Vocabulary and function words are independent, so each mismatch, assuming separate authorship is at most 10% probable, otherwise the perfect match in the other play identifications is not reasonable. There are 5 mismatched plays, so a probability of $10^{-5}$ of different authorship under these generous assumptions (it is probably closer to 1 in $10^10$), so the chance is more like 1 in 100,000.
Co-authorship?
The only other hypothesis that is reasonable is that Shakespeare modified existing unfinished texts of unpublished Marlowe's plays into his early works. This is unlikely, considering that there is no sharp break in style between Shakespeare and Shakespeare. If one attributes the Shakespeare canon to one author, which I am sure is correct, one must attribute it to Marlowe, with at least 4 sigma confidence level, probably much more.
Their Dubious Conclusion
The content of their computer experiments are an unacceptable counterpoint to their conclusion. Their methods classified nearly all of Marlowe dramatical works, other but the Tambourlaines, as Shakespeare, consistently in both methods, and over two different trials.
From this failure, I feel confident to conclude, unlike these authors, that there is no stylometric difference between Shakespeare and Marlowe, and it is nearly certain in the scientific sense that Marlowe and Shakespeare are the same person.
I am not sure this exhausts the question, considering that these authors are not so reliable, having published a paper with contents and conclusion diametrically opposed. A further more neutral study, even just a replication of their methods with a more quantitative Bayesian estimate of identity, would be useful.