##### Thomas Bayes

- This statistical method is named for Thomas Bayes who first formulated the basic process, which is this: begin with an estimate of the probability that any claim, belief, hypothesis is true, then look at any new data and update the probability given the new data. (theness.com)
- The Reverend Thomas Bayes died 250 years ago this month. (r-bloggers.com)
- The series kicks off with the tribute to Thomas Bayes below. (r-bloggers.com)
- Thomas Bayes was the son of London Presbyterian minister Joshua Bayes, and was possibly born in Hertfordshire. (wikipedia.org)
- While it is certain to have been discovered before Thomas Bayes' time, there are several contenders for priority including Saunderson. (wikipedia.org)
- The fundamental ideas and concepts behind Bayes' theorem, and its use within Bayesian inference, have been developed and added to over the past centuries by Thomas Bayes, Richard Price and Pierre Simon Laplace as well as numerous other mathematicians, statisticians and scientists. (wikipedia.org)
- Bayes's theorem is named after Rev. Thomas Bayes 1701-1761. (wikipedia.org)
- The term Bayesian derives from the 18th century mathematician and theologian Thomas Bayes, who provided the first mathematical treatment of a non-trivial problem of Bayesian inference. (wikipedia.org)

##### Bayes's Theorem

- James Rock explains how he's using Bayes's Theorem to fit data to a parametric distribution with Mathematica in this talk from the Wolfram Technology Conference. (wolfram.com)
- I think 'Bayes' Theorem' (but perhaps not Bayes's Theorem ) is catchier than the latter two suggestions. (lesswrong.com)
- Who discovered Bayes's theorem? (wikipedia.org)
- 24 November - Thomas Bayes's theorem is first announced (posthumously). (wikipedia.org)
- More formally, the same probability of roughly 0.02 can be established using Bayes's theorem. (wikipedia.org)
- In addition, the pair used ping-pong balls to demonstrate Bayes's theorem. (wikipedia.org)
- The jury was instructed in the use of Bayes's theorem by Professor Peter Donnelly of Oxford University. (wikipedia.org)
- The judge told the jury they could use Bayes's theorem if they wished. (wikipedia.org)
- The Appeal Court judges noted that the original trial judge did not direct the jury as to what to do if they did not wish to use Bayes's theorem and ordered a retrial. (wikipedia.org)
- At the retrial the defence team again wanted to instruct the new jury in the use of Bayes's theorem (though Prof. Donnelly had doubts about the practicality of the approach). (wikipedia.org)
- The judge asked that the statistical experts from both sides work together to produce a workable method of implementing Bayes's theorem for use in a courtroom, should the jury wish to use it. (wikipedia.org)
- The appeal was unsuccessful and the Appeal Court ruling was highly critical of the appropriateness of Bayes's theorem in the courtroom. (wikipedia.org)

##### Bayesian

- Bayesian theory in E-discovery - the application of Bayes' theorem in legal evidence diagnostics and E-discovery, where it provides a way of updating the probability of an event in the light of new information. (wikipedia.org)
- Bayesian theory in marketing - the application of Bayes' theorem in marketing, where it allows for decision making and market research evaluation under uncertainty and limited data. (wikipedia.org)
- Bayesian skeptics have objected to this use of Bayes' theorem in litigation on a variety of grounds. (wikipedia.org)
- Here's an explanation of how to use Bayes' Rule in simple situations, and introduce the relationship between Bayesian and frequentist probability. (decodedscience.org)
- Bayes' theorem is fundamental to Bayesian inference. (wikipedia.org)
- For objectivists, interpreting probability as extension of logic, probability quantifies the reasonable expectation everyone (even a "robot") sharing the same knowledge should share in accordance with the rules of Bayesian statistics, which can be justified by Cox's theorem. (wikipedia.org)
- In Bayesian statistics, the theorem itself plays a more limited role. (wikipedia.org)

##### conditional probability

- What is conditional probability and Bayes' theorem? (coursera.org)
- Use the Bayes Rule Calculator to compute conditional probability, when Bayes' theorem can be applied. (stattrek.com)
- In Lesson 2, we review the rules of conditional probability and introduce Bayes' theorem. (coursera.org)

##### Rule

- Bayes' theorem (also known as Bayes' rule) is a useful tool for calculating conditional probabilities . (stattrek.com)
- Reminds me of something I saw a few years ago: a student came to a meeting with pretty bad translation results when correctly using Bayes' rule. (johndcook.com)
- formulating it in terms of likelihoods and Bayes' rule is really less of a formalism and more of a framework that provides some constraints that are useful for limiting the search space. (johndcook.com)
- Bayes' theorem is a rule in probability and statistical theory that calculates an event's probability based on related conditions or events. (decodedscience.org)
- In frequentist statistics, Bayes' theorem provides a useful rule for updating a probability when new frequency data becomes available. (wikipedia.org)
- In fact, that step, Bayes' rule of updating, can be justified, as necessary and sufficient, through a dynamic Dutch book argument that is additional to the arguments used to justify the probability axioms. (wikipedia.org)
- In this case Bayes' rule isn't able to capture a mere subjective change in the probability of some critical fact. (wikipedia.org)

##### 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)

##### statistical

- I have written a little about Bayes Theorem, mainly on Science-Based Medicine, which is a statistical method for analyzing data. (theness.com)
- However, there are some statistical nuances when applying Bayes to specific scientific situations. (theness.com)
- This section presents an example that demonstrates how Bayes' theorem can be applied effectively to solve statistical problems. (stattrek.com)
- Professor Stephen Stigler, historian of statistical science, thinks that Bayes became interested in the subject while reviewing a work written in 1755 by Thomas Simpson, but George Alfred Barnard thinks he learned mathematics and probability from a book by Abraham de Moivre. (wikipedia.org)
- The theorem provides a formal reconciliation between judgment expressed quantitatively in the prior distribution and the statistical evidence of the experiment. (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)

##### posthumously

- In addition, a paper by Bayes on asymptotic series was published posthumously. (wikipedia.org)

##### inverse

- The use of evidence under Bayes' theorem relates to the likelihood of finding evidence in relation to the accused, where Bayes' theorem concerns the probability of an event and its inverse. (wikipedia.org)
- Bayes' solution to a problem of inverse probability was presented in "An Essay towards solving a Problem in the Doctrine of Chances" which was read to the Royal Society in 1763 after Bayes' death. (wikipedia.org)

##### subjective

- Bayes theorem may refer to: Bayes' theorem - a theorem which expresses how a subjective degree of belief should rationally change to account for evidence. (wikipedia.org)

##### statistics

- This month, Revolution Analytics' partner IBM Netezza commemorates Bayes' contributions to Statistics with a series of videos on Bayes Theorem, its applications, and the implications for Big Data and predictive analytics. (r-bloggers.com)
- According to one historian of statistics, he may have been the earliest discoverer of Bayes theorem. (wikipedia.org)
- It was Pierre-Simon Laplace (1749-1827) who introduced a general version of the theorem and used it to approach problems in celestial mechanics, medical statistics, reliability, and jurisprudence. (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)

##### calculate

- That is exactly what Bayes seeks to calculate. (theness.com)

##### application

- The assumption of equivalent confidence is necessary to justify application of Bayes' theorem to any finite sample. (johndcook.com)
- These methods allow information theory to be related to probability, in a way that can be compared to the application of Bayes' theorem, but which give a source and explanation for the role of prior probabilities. (wikipedia.org)

##### However

- However, adopting Bayes' theorem is a temptation. (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)

##### problems

- We define and apply the central limit theorem to sampling problems and brieflyt- and c2. (coursera.org)
- Part of the challenge in applying Bayes' theorem involves recognizing the types of problems that warrant its use. (stattrek.com)

##### 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)

##### basic

- That is really the basic concept of Bayes Theorem. (theness.com)

##### apply

- We then give the definitions of probability and the laws governing it and apply Bayes theorem. (coursera.org)
- The remainder of this lesson covers material that can help you understand when and how to apply Bayes' theorem effectively. (stattrek.com)
- But this theorem is sometimes hard to apply and understand. (wikipedia.org)

##### example

- Bayes' theorem can be best understood through an example. (stattrek.com)

##### terms

- How our plausible reasoning can be interpreted in terms of Bayes' theorem? (coursera.org)

##### sometimes

- sometimes used for the Bayes Theorem probability. (coursera.org)

##### special

- This essay contains a statement of a special case of Bayes' theorem. (wikipedia.org)

##### famous

- There are some famous cases where Bayes' theorem can be applied. (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)

##### below

- The answer can be determined from Bayes' theorem, as shown below. (stattrek.com)

##### module

- In this module, we review the basics of probability and Bayes' theorem. (coursera.org)

##### 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)

##### consider

- You should consider Bayes' theorem when the following conditions exist. (stattrek.com)

##### find

- No, for the same reason we aren't surprised when we find that logistic regression outperforms naive Bayes. (johndcook.com)

##### topic

- the next topic I want to look at is Bayes Theorem. (coursera.org)
- The discovery of Bayes' theorem remains a controversial topic in the history of mathematics. (wikipedia.org)

##### 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)

##### work

- Also, work on Bayes nets continues. (wikipedia.org)

##### held

- Bayes' theorem connects probabilities that are held simultaneously. (wikipedia.org)

##### probability

- Naive Bayes classifiers work by correlating the use of tokens (typically words, or sometimes other things), with spam and non-spam e-mails and then using Bayes' theorem to calculate a probability that an email is or is not spam. (wikipedia.org)
- This contribution is called the posterior probability and is computed using Bayes' theorem. (wikipedia.org)
- The Bayes factor is a ratio of the likelihood probability of two competing hypotheses, usually a null and an alternative. (wikipedia.org)
- Professor Stephen Stigler, historian of statistical science, thinks that Bayes became interested in the subject while reviewing a work written in 1755 by Thomas Simpson, but George Alfred Barnard thinks he learned mathematics and probability from a book by Abraham de Moivre. (wikipedia.org)
- Bayes' solution to a problem of inverse probability was presented in "An Essay towards solving a Problem in the Doctrine of Chances" which was read to the Royal Society in 1763 after Bayes' death. (wikipedia.org)

##### Bayesian

- CRM114, oft cited as a Bayesian filter, is not intended to use a Bayes filter in production, but includes the ″unigram″ feature for reference. (wikipedia.org)
- Bayesian email filters utilize Bayes' theorem. (wikipedia.org)
- In statistics, the use of Bayes factors is a Bayesian alternative to classical hypothesis testing. (wikipedia.org)
- Bayesian model comparison is a method of model selection based on Bayes factors. (wikipedia.org)
- For models where an explicit version of the likelihood is not available or too costly to evaluate numerically, approximate Bayesian computation can be used for model selection in a Bayesian framework, with the caveat that approximate-Bayesian estimates of Bayes factors are often biased. (wikipedia.org)
- Bayesian procedures, including Bayes factors, are coherent, so there is no need to draw such a distinction. (wikipedia.org)
- For decision-making, Bayesian statisticians might use a Bayes factor combined with a prior distribution and a loss function associated with making the wrong choice. (wikipedia.org)

##### displaystyle

- Bayes' theorem can be applied to a pair of competing models M 1 {\displaystyle M_{1}} and M 2 {\displaystyle M_{2}} for data D {\displaystyle D} , one of which may be true (though which one is unknown) but which both cannot be true simultaneously. (wikipedia.org)
- The remaining Bayes factor P ( D ∣ M 2 ) / P ( D ∣ M 1 ) {\displaystyle P(D\mid M_{2})/P(D\mid M_{1})} is not so easy to evaluate, since in general it requires marginalizing nuisance parameters. (wikipedia.org)
- When the two models are equally probable a priori, so that Pr ( M 1 ) = Pr ( M 2 ) {\displaystyle \Pr(M_{1})=\Pr(M_{2})} , the Bayes factor is equal to the ratio of posterior probabilities of M1 and M2. (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)

##### approach

- and emerging theoretical concepts such as the PAC-Bayes approach and compression-based bounds. (barnesandnoble.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)
- This essay contains a statement of a special case of Bayes' theorem. (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)