• ##### 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)
• ##### data
• In Peter Norvig's talk The Unreasonable Effectiveness of Data, starting at 37:42, he describes a translation algorithm based on Bayes' theorem. (johndcook.com)
• ##### 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)
• ##### likelihood
• If she used Bayes' theorem, she could multiply those prior odds by a "likelihood ratio" in order to update her odds after learning that the hair matched the defendant's hair. (wikipedia.org)
• ##### evidence
• This is one of the things I really like about Bayes - it expressly considers the probability that a claim is true given everything we know about the universe, and then puts new evidence into the context of that prior probability. (theness.com)
• First, they have said that whatever its value in litigation, Bayes' theorem is valuable in studying evidence rules. (wikipedia.org)
• Second, they have said that it is practical to use Bayes' theorem in a limited set of circumstances in litigation (such as integrating genetic match evidence with other evidence), and that assertions that probability theory is inappropriate for judicial determinations are nonsensical or inconsistent. (wikipedia.org)
• These questions were intended to allow the Bayes factors of the various pieces of evidence to be assessed. (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 Lemaître 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)
• ##### applications
• You will never be able to fit all of the applications of Bayes Theorem in one hour so pick one or two and make it look awesome. (lesswrong.com)
• Because since then, Bayes Theorem has been the underpinning of predictive analytics applications from spam detection to medical alerts. (r-bloggers.com)
• ##### decision
• the constraints are justified by the Dutch book argument or by the decision theory and de Finetti's theorem. (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)
• ##### 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)
• ##### 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)
• ##### appears
• At first sight Bayes' theorem appears different from the minimimum message/description length principle. (wikipedia.org)
• ##### find
• No, for the same reason we aren't surprised when we find that logistic regression outperforms naive Bayes. (johndcook.com)
• ##### problem
• So, this is a problem that we'll utilize Bayes Theorem that we've already given. (coursera.org)
• Bayes' "Essay" contains his solution to a similar problem posed by Abraham de Moivre, author of The Doctrine of Chances (1718). (wikipedia.org)
• ##### statistical
• Naive Bayes classifiers are a popular statistical technique of e-mail filtering. (wikipedia.org)
• If instead of the Bayes factor integral, the likelihood corresponding to the maximum likelihood estimate of the parameter for each statistical model is used, then the test becomes a classical likelihood-ratio test. (wikipedia.org)
• ##### fundamental
• The course will cover limits, continuity, differentiation, applications of derivatives, introduction to integration, techniques of integration and the fundamental theorem of calculus. (highpoint.edu)
• ##### assumptions
• In this second letter Selvin proposed a solution based on Bayes' theorem and explicitly outlined some assumptions concerning the moderator's behavior. (wikipedia.org)
• Both theories derive a best linear unbiased estimator, based on assumptions on covariances, make use of Gauss-Markov theorem to prove independence of the estimate and error, and make use of very similar formulae. (wikipedia.org)
• ##### geometry
• c. 300 BC - Euclid's Elements expound geometry as a system of theorems following logically from axioms known with certainty. (wikipedia.org)
• ##### context
• An alternative table, widely cited, is provided by Kass and Raftery (1995): The use of Bayes factors or classical hypothesis testing takes place in the context of inference rather than decision-making under uncertainty. (wikipedia.org)
• ##### factor
• The aim of the Bayes factor is to quantify the support for a model over another, regardless of whether these models are correct. (wikipedia.org)
• ##### solution
• Bayes' "Essay" contains his solution to a similar problem posed by Abraham de Moivre, author of The Doctrine of Chances (1718). (wikipedia.org)
• ##### includes
• However, an advantage of the use of Bayes factors is that it automatically, and quite naturally, includes a penalty for including too much model structure. (wikipedia.org)