• Cox's
• It would be cool if you found a way to work in the existence of Cox's theorem -- when I encountered it, I had never thought about why the laws of probability were given as they are, or if there could be a different consistent way to represent and calculate probability besides multiplying numbers together. (lesswrong.com)
• According to the objectivist view, probability is a reasonable expectation that represents the state of knowledge, can be interpreted as an extension of logic, and its rules can be justified by Cox's theorem. (wikipedia.org)
• posterior
• 2) While Bayes' theorem describes a way of obtaining the actual posterior probability, maximizing that is only loosely related to any downstream loss function you actually care about, and there are decision-theoretic reasons to add extra parameters (a temperature in this case) to your model to improve a downstream loss. (johndcook.com)
• and based directly on Bayes theorem, it allows us to make better posterior estimates as more observations become available. (wikipedia.org)
• Mathematical
• It says, "Mathematical formulas and theorems are usually not named after their original discoverers" and was named after Carl Boyer, whose book History of Mathematics contains many examples of this law. (wikipedia.org)
• jury
• Some observers believe that in recent years (i) the debate about probabilities has become stagnant, (ii) the protagonists in the probabilities debate have been talking past each other, (iii) not much is happening at the high-theory level, and (iv) the most interesting work is in the empirical study of the efficacy of instructions on Bayes' theorem in improving jury accuracy. (wikipedia.org)
• view
• According to the subjectivist view, probability quantifies a personal belief, and its rules can be justified by requirements of rationality and coherence following from the Dutch book argument or from the decision theory and de Finetti's theorem. (wikipedia.org)
• things
• At the moment, I'm thinking about how to design the class, so I'd appreciate any suggestions as to what content I should cover, the best format, clear ways to explain it, cool things related to Bayes' Theorem, good links, and so forth. (lesswrong.com)
• case
• c. 1701 - 7 April 1761) was an English statistician, philosopher and Presbyterian minister who is known for having formulated a specific case of the theorem that bears his name: Bayes' theorem. (wikipedia.org)
• known
• Examples include Hubble's law which was derived by Georges LemaĆ®tre two years before Edwin Hubble, the Pythagorean theorem although it was known to Babylonian mathematicians before Pythagoras, and Halley's comet which was observed by astronomers since at least 240 BC. (wikipedia.org)
• better
• So we experimented some, and we found out that when you raise that first factor [in Bayes' theorem] to the 1.5 power, you get a better result. (johndcook.com)
• List
• Eponym List of examples of Stigler's law List of misnamed theorems List of persons considered father or mother of a scientific field Matthew effect Matilda effect Obliteration by incorporation Scientific priority Standing on the shoulders of giants Theories and sociology of the history of science Gieryn, T. F., ed. (1980). (wikipedia.org)
• simple
• Later on, it turned out to have been a simple mistake -- the test was a false positive, and the 999 out of 1,000 figure had been based on a lack of understanding about Bayes' Theorem. (lesswrong.com)
• find
• No, for the same reason we aren't surprised when we find that logistic regression outperforms naive Bayes. (johndcook.com)