Bayes' Theorem or Bayes's Theorem? (Similarly, Charles' Law or Charles's Law?) [duplicate]
If Bayes had discovered it today, we might call it Bayes's theorem, pronounced baizes to rhyme with mazes. However, Thomas Bayes lived in the 18th century, and the theorem was published in 1763. I believe that before the 20th century, the rules for pronouncing possessives may have been slightly different (this isn't completely standardized; different people still treat the pronunciation of possessives like Jones'(s) differently today), so we call it Bayes' theorem, pronounced bays to rhyme with maze. Note that in the Wikipedia article I linked to they use Bayes's death, but Bayes' theorem.
The earliest reference I can find in Google books to Bayes' rule (1854) spells it Bayes's. However, it seems that when it became widely discussed in the early 1900s with increased investigation of probability, it was generally referred to as Bayes'.
This Ngram shows that before around 1900, Charles's was the dominant spelling, but after 1900, Charles' became more common.
You will find many grammarians who tell you that if the noun ends in s and is singular, an 's is still used. This is disputable, as per this wikipedia discussion:
If a singular noun ends with an s-sound (spelt with -s, -se, for example), practice varies as to whether to add 's or the apostrophe alone. A widely accepted practice is to follow whichever spoken form is judged better: the boss's shoes, Mrs Jones' hat (or Mrs Jones's hat, if that spoken form is preferred). In many cases, both spoken and written forms differ between writers.
My best advice is: be consistent.