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Cromwell's Rule
Cromwell's rule, named by statistician Dennis Lindley, states that the use of prior probabilities of 1 ("the event will definitely occur") or 0 ("the event will definitely not occur") should be avoided, except when applied to statements that are logically true or false, such as equaling 4. The reference is to Oliver Cromwell, who wrote to the General Assembly of the Church of Scotland on 3 August 1650, shortly before the Battle of Dunbar, including a phrase that has become well known and frequently quoted: As Lindley puts it, assigning a probability should "leave a little probability for the moon being made of green cheese; it can be as small as 1 in a million, but have it there since otherwise an army of astronauts returning with samples of the said cheese will leave you unmoved". Similarly, in assessing the likelihood that tossing a coin will result in either a head or a tail facing upwards, there is a possibility, albeit remote, that the coin will land on its edge a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dennis Lindley
Dennis Victor Lindley (25 July 1923 – 14 December 2013) was an English statistician, decision theorist and leading advocate of Bayesian statistics. Biography Lindley grew up in the south-west London suburb of Surbiton. He was an only child and his father was a local building contractor. Lindley recalled (to Adrian Smith) that the family had "little culture" and that both his parents were "proud of the fact that they had never read a book". The school Lindley attended, Tiffin School, introduced him to "ordinary cultural activities"."Lindley Prize – Dennis Lindley" International Society for Bayesian Analysis, ''accessed 31 October 2023'' From there Lindley went t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prior Probability
A prior probability distribution of an uncertain quantity, simply called the prior, is its assumed probability distribution before some evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election. The unknown quantity may be a parameter of the model or a latent variable rather than an observable variable. In Bayesian statistics, Bayes' rule prescribes how to update the prior with new information to obtain the posterior probability distribution, which is the conditional distribution of the uncertain quantity given new data. Historically, the choice of priors was often constrained to a conjugate family of a given likelihood function, so that it would result in a tractable posterior of the same family. The widespread availability of Markov chain Monte Carlo methods, however, has made this less of a concern. There are many ways to const ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oliver Cromwell
Oliver Cromwell (25 April 15993 September 1658) was an English statesman, politician and soldier, widely regarded as one of the most important figures in British history. He came to prominence during the Wars of the Three Kingdoms, initially as a senior commander in the Parliamentarian army and latterly as a politician. A leading advocate of the execution of Charles I in January 1649, which led to the establishment of the Commonwealth of England, Cromwell ruled as Lord Protector from December 1653 until his death. Although elected Member of Parliament (MP) for Huntingdon in 1628, much of Cromwell's life prior to 1640 was marked by financial and personal failure. He briefly contemplated emigration to New England, but became a religious Independent in the 1630s and thereafter believed his successes were the result of divine providence. In 1640 he was returned as MP for Cambridge in the Short and Long Parliaments. He joined the Parliamentarian army when the First Engl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Church Of Scotland
The Church of Scotland (CoS; ; ) is a Presbyterian denomination of Christianity that holds the status of the national church in Scotland. It is one of the country's largest, having 245,000 members in 2024 and 259,200 members in 2023. While membership in the church has declined significantly in recent decades (in 1982 it had nearly 920,000 members), the government Scottish Household Survey found that 20% of the Scottish population, or over one million people, identified the Church of Scotland as their religious identity in 2019. In the 2022 census, 20.4% of the Scottish population, or 1,108,796 adherents, identified the Church of Scotland as their religious identity. The Church of Scotland's governing system is Presbyterian polity, presbyterian in its approach, therefore, no one individual or group within the church has more or less influence over church matters. There is no one person who acts as the head of faith, as the church believes that role is the "Lord God's". As a pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Battle Of Dunbar (1650)
The Battle of Dunbar was fought between the English New Model Army, under Oliver Cromwell, and a Scottish army commanded by David Leslie, 1st Lord Newark, David Leslie on 3 September 1650 near Dunbar, Scotland. The battle resulted in a decisive victory for the English. It was the first major battle of the Anglo-Scottish war (1650–1652), 1650 invasion of Scotland, which was triggered by Scotland's acceptance of Charles II of England, Charles II as king of Britain after the beheading of his father, Charles I of England, Charles I on 30 January 1649. After Charles I's execution, the English Rump Parliament established a republican Commonwealth of England, Commonwealth in England. When their Solemn League and Covenant, erstwhile ally, Scotland, recognised Charles II as king of all of Britain on 1 May 1650 and began recruiting an army to support him, the English dispatched the New Model Army, under the command of Cromwell. The army crossed into Scotland on 22 July, with a fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Moon Is Made Of Green Cheese
"The Moon is made of green cheese" is a statement referring to a fanciful belief that the Moon is composed of cheese. In its original formulation as a proverb and metaphor for credulity with roots in fable, this refers to the perception of a simpleton who sees a reflection of the Moon in water and mistakes it for a round cheese wheel. It is widespread as a folkloric motif among many of the world's cultures, and the notion has also found its way into children's folklore and modern popular culture. The phrase " green cheese" in the common version of this proverb (sometimes "cream cheese" is used), may refer to a young, unripe cheese or to cheese with a greenish tint. There was never an actual historical popular belief that the Moon is made of green cheese (''cf.'' Flat Earth and the myth of the flat Earth). It was typically used as an example of extreme credulity, a meaning that was clear and commonly understood as early as 1638. Fable There exists a family of stories, in com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayes' Theorem
Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting Conditional probability, conditional probabilities, allowing one to find the probability of a cause given its effect. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to someone of a known age to be assessed more accurately by conditioning it relative to their age, rather than assuming that the person is typical of the population as a whole. Based on Bayes' law, both the prevalence of a disease in a given population and the error rate of an infectious disease test must be taken into account to evaluate the meaning of a positive test result and avoid the ''base-rate fallacy''. One of Bayes' theorem's many applications is Bayesian inference, an approach to statistical inference, where it is used to invert the probability of Realization (probability), observations given a model configuration (i.e., th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Posterior Probability
The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood via an application of Bayes' rule. From an epistemological perspective, the posterior probability contains everything there is to know about an uncertain proposition (such as a scientific hypothesis, or parameter values), given prior knowledge and a mathematical model describing the observations available at a particular time. After the arrival of new information, the current posterior probability may serve as the prior in another round of Bayesian updating. In the context of Bayesian statistics, the posterior probability distribution usually describes the epistemic uncertainty about statistical parameters conditional on a collection of observed data. From a given posterior distribution, various point and interval estimates can be derived, such as the maximum a posteriori (MAP) or the highest posterior density int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Inference
Bayesian inference ( or ) is a method of statistical inference in which Bayes' theorem is used to calculate a probability of a hypothesis, given prior evidence, and update it as more information becomes available. Fundamentally, Bayesian inference uses a prior distribution to estimate posterior probabilities. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability". Introduction to Bayes' rule Formal explanation Bayesian inference derives the posterior probability as a consequence of two antecedents: a prior probability and a "likelihood function" derive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Why So Many Predictions Fail – But Some Don't
Why may refer to: * Causality, a consequential relationship between two events * Reason (argument), a premise in support of an argument, for what reason or purpose * Grounding (metaphysics), a topic in metaphysics regarding how things exist in virtue of more fundamental things. * Why?, one of the Five Ws used in journalism Music Artists * Why? (American band), a hip hop/indie rock band formed in Oakland, California, in 2004 ** Yoni Wolf, formerly known by the stage name Why? * Why (Canadian band), a rock band formed in Winnipeg, Manitoba, in 1993 * Why?, a 1990s UK folk band, two members of which formed Quench in 2001 Albums * ''Why'' (Baby V.O.X album) or the title song, 2000 * ''Why?'' (Ginger Baker album) or the title song, 2014 * ''Why'' (Prudence Liew album) or the title song, 1987 * ''Why?'' (They Might Be Giants album), 2015 * ''Why?'', by Jacob Whitesides, 2016 * ''Why'', by Moahni Moahna, 1996 * ''Why?'', by the MonaLisa Twins, 2022 EPs * ''Why'' (Discharge EP ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Additive Smoothing
In statistics, additive smoothing, also called Laplace smoothing or Lidstone smoothing, is a technique used to smooth count data, eliminating issues caused by certain values having 0 occurrences. Given a set of observation counts \mathbf = \langle x_1, x_2, \ldots, x_d \rangle from a d-dimensional multinomial distribution with N trials, a "smoothed" version of the counts gives the estimator : \hat\theta_i = \frac \qquad (i = 1, \ldots, d), where the smoothed count \hat x_i = N \hat\theta_i, and the "pseudocount" ''α'' > 0 is a smoothing parameter, with ''α'' = 0 corresponding to no smoothing (this parameter is explained in below). Additive smoothing is a type of shrinkage estimator, as the resulting estimate will be between the empirical probability ( relative frequency) x_i/N and the uniform probability 1/d. Common choices for ''α'' are 0 (no smoothing), (the Jeffreys prior), or 1 (Laplace's rule of succession), but the parameter may also be set empi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
