**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)
- This week: some of my favorite problems involving Bayes's Theorem. (blogspot.com)
- It is simple enough to solve without Bayes's Theorem, but good for practice. (blogspot.com)
- 2) It should make good use of Bayes's Theorem -- that is, it should be easier to solve with BT than without. (blogspot.com)
- This in-depth discussion of New Testament scholarship and the challenges of history as a whole proposes Bayes's Theorem, which deals with probabilities under conditions of uncertainty, as a solution to the problem of establishing reliable historical criteria. (idreambooks.com)
- The author demonstrates that valid historical methods-not only in the study of Christian origins but in any historical study-can be described by, and reduced to, the logic of Bayes's Theorem. (idreambooks.com)
- Writing with thoroughness and clarity, the author explains Bayes's Theorem in terms that are easily understandable to professional historians and laypeople alike, employing nothing more than well-known primary school math. (idreambooks.com)
- The author demonstrates not only the deficiencies of these approaches but also ways to rehabilitate them using Bayes's Theorem. (idreambooks.com)
- Anyone with an interest in historical methods, how historical knowledge can be justified, new applications of Bayes's Theorem, or the study of the historical Jesus will find this book to be essential reading. (idreambooks.com)
- The top response, which uses Bayes's Theorem, is correct. (blogspot.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)
- One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference. (wikipedia.org)
- With the Bayesian probability interpretation the theorem expresses how a subjective degree of belief should rationally change to account for availability of related evidence. (wikipedia.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)

**probabilities**- Bayes' theorem (also known as Bayes' rule) is a useful tool for calculating conditional probabilities . (stattrek.com)
- 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)
- When applied, the probabilities involved in Bayes' theorem may have different probability interpretations. (wikipedia.org)
- But Bayes' theorem always depended on prior probabilities, to generate new probabilities. (wikipedia.org)
- 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)
- Bayes' theorem is about conditional probabilities. (wikipedia.org)
- Bayes' theorem connects probabilities that are held simultaneously. (wikipedia.org)

**compute**- Use the Bayes Rule Calculator to compute conditional probability, when Bayes' theorem can be applied. (stattrek.com)
- Suppose you're given following dataset which has unknown label and your task is to use training dataset and Naive Bayes algorithm to compute label for an unknown record. (ghost.io)

**algorithm**- 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)
- Sir Harold Jeffreys put Bayes' algorithm and Laplace's formulation on an axiomatic basis. (wikipedia.org)
- Today I am going to write off-topic about using Naive Bayes algorithm for record classification. (ghost.io)

**Pythagorean**- 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)

**mathematically**- Bayes also shows mathematically why confirmatory tests are so powerful. (theness.com)

**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)

**probability theory**- Bayes' theorem is an elementary proposition of probability theory. (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)
- In probability theory and statistics, Bayes' theorem is a concept where there are two distinct interpretations. (brainmass.com)
- In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule) describes the probability of an event, based on prior knowledge of conditions that might be related to the event. (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)

**Rule**- 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)
- 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)

**likelihood**- 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)
- 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)
- Each friend is twice as likely to tell the truth as to lie, so each friend contributes evidence in favor of rain with a likelihood ratio, or Bayes factor, of 2. (blogspot.com)

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

**inverse**- 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)

**data**- 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)

**statistics**- 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)

**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)

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

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

**View**- 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)
- 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)

**application**- The assumption of equivalent confidence is necessary to justify application of Bayes' theorem to any finite sample. (johndcook.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)
- These questions were intended to allow the Bayes factors of the various pieces of evidence to be assessed. (wikipedia.org)

**problems**- Part of the challenge in applying Bayes' theorem involves recognizing the types of problems that warrant its use. (stattrek.com)

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

**concepts**- Use probability concepts found in Bayes' Theorem to formulate a decision. (brainmass.com)

**decision**- the constraints are justified by the Dutch book argument or by the decision theory and de Finetti's theorem. (wikipedia.org)

**special case**- 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)

**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)

**Author**- Bayes' "Essay" contains his solution to a similar problem posed by Abraham de Moivre, author of The Doctrine of Chances (1718). (wikipedia.org)

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

**different**- At first sight Bayes' theorem appears different from the minimimum message/description length principle. (wikipedia.org)

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

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

**apply**- 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)
- For example, if cancer is related to age, then, using Bayes' theorem, a person's age can be used to more accurately assess the probability that they have cancer, compared to the assessment of the probability of cancer made without knowledge of the person's age. (wikipedia.org)

**make**- He then explores precisely how the theorem can be applied to history and addresses numerous challenges to and criticisms of its use in testing or justifying the conclusions that historians make about the important persons and events of the past. (idreambooks.com)

**basis**- The basis of inference is Bayes' theorem. (wikipedia.org)

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

**problem**- problem 11)a) (i) Define Bayes theorem. (mywordsolution.com)

**looks**- theorem which looks at the probability of occurrence of events as the outcome of the previous events. (brainmass.com)

**methods**- The traditional and established methods of historians are analyzed using the theorem, as well as all the major "historicity criteria" employed in the latest quest to establish the historicity of Jesus. (idreambooks.com)

**interest**- One area of particular interest and controversy has been Bayes' theorem. (wikipedia.org)

**medical**- Because since then, Bayes Theorem has been the underpinning of predictive analytics applications from spam detection to medical alerts. (r-bloggers.com)

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