|
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 2+2 equaling 4 or 5. 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 edg ... [...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.""The Lindley Prize – Dennis V. Lindley" International Society for ...
[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prior Probability
In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity 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. Bayes' theorem calculates the renormalized pointwise product of the prior and the likelihood function, to produce the ''posterior probability distribution'', which is the conditional distribution of the uncertain quantity given the data. Similarly, the prior probability of a random event or an uncertain proposition is the unconditional probability that is assigned before any relevant evidence is taken into account. Priors can be created using a n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oliver Cromwell
Oliver Cromwell (25 April 15993 September 1658) was an English politician and military officer who is widely regarded as one of the most important statesmen in English history. He came to prominence during the 1639 to 1651 Wars of the Three Kingdoms, first as a senior commander in the Parliamentarian army and then as a politician. A leading advocate of the execution of Charles I in January 1649, which led to the establishment of the Republican Commonwealth of England, Scotland and Ireland, he ruled as Lord Protector from December 1653 until his death in September 1658. Cromwell nevertheless remains a deeply controversial figure in both Britain and Ireland, due to his use of the military to first acquire, then retain political power, and the brutality of his 1649 Irish campaign. Educated at Sidney Sussex College, Cambridge, Cromwell was elected MP for Huntingdon in 1628, but the first 40 years of his life were undistinguished and at one point he contemplated emigrati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Church Of Scotland
The Church of Scotland ( sco, The Kirk o Scotland; gd, Eaglais na h-Alba) is the national church in Scotland. The Church of Scotland was principally shaped by John Knox, in the Reformation of 1560, when it split from the Catholic Church and established itself as a church in the reformed tradition. The church is Calvinist Presbyterian, having no head of faith or leadership group and believing that God invited the church's adherents to worship Jesus. The annual meeting of its general assembly is chaired by the Moderator of the General Assembly of the Church of Scotland. The Church of Scotland celebrates two sacraments, Baptism and the Lord's Supper, as well as five other rites, such as Confirmation and Matrimony. The church adheres to the Bible and the Westminster Confession of Faith, and is a member of the World Communion of Reformed Churches. History Presbyterian tradition, particularly that of the Church of Scotland, traces its early roots to the church founded ... [...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, 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 1650 invasion of Scotland, which was triggered by Scotland's acceptance of Charles II as king of Britain after the beheading of his father, Charles I on 30 January 1649. After Charles I's execution, the English Rump Parliament established a republican Commonwealth in England. When their 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 force of over 16,000 men. The Scots withdrew to Edinburgh, stripping the land of provisions. Cromwell attempted to draw the Scots out into a set piece battle, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Moon Being 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 compara ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayes' Theorem
In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual of a known age to be assessed more accurately (by conditioning it on their age) than simply assuming that the individual is typical of the population as a whole. One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference. When applied, the probabilities involved in the theorem may have different probability interpretations. With Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence. Bayesian inference is fundamental to Bayesia ... [...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 interval (HP ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Inference
Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. 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" derived from a statistical model for the observed data. Bayesian inference computes the posterior probability according to Bayes' theorem ... [...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) o ... [...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 categorical data. Given a set of observation counts \textstyle from a \textstyle -dimensional multinomial distribution with \textstyle trials, a "smoothed" version of the counts gives the estimator: :\hat\theta_i= \frac \qquad (i=1,\ldots,d), where the smoothed count \textstyle and the "pseudocount" ''α'' > 0 is a smoothing parameter. ''α'' = 0 corresponds 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) \textstyle , and the uniform probability \textstyle . Invoking Laplace's rule of succession, some authors have argued that ''α'' should be 1 (in which case the term add-one smoothing is also used), though in practice a smaller value is typically chosen. From a Bayesian point of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule Of Succession
In probability theory, the rule of succession is a formula introduced in the 18th century by Pierre-Simon Laplace in the course of treating the sunrise problem. The formula is still used, particularly to estimate underlying probabilities when there are few observations or for events that have not been observed to occur at all in (finite) sample data. Statement of the rule of succession If we repeat an experiment that we know can result in a success or failure, ''n'' times independently, and get ''s'' successes, and ''n − s'' failures, then what is the probability that the next repetition will succeed? More abstractly: If ''X''1, ..., ''X''''n''+1 are conditionally independent random variables that each can assume the value 0 or 1, then, if we know nothing more about them, :P(X_=1 \mid X_1+\cdots+X_n=s)=. Interpretation Since we have the prior knowledge that we are looking at an experiment for which both success and failure are possible, our estimate is as if we had ob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.jpg "Click for more on -> The Moon Being Made Of Green Cheese")
