• algorithmic
• Ray Solomonoff developed algorithmic probability which gave an explanation for what randomness is and how patterns in the data may be represented by computer programs, that give shorter representations of the data circa 1964. (wikipedia.org)
• principle of indiffere
• In the classical interpretation, probability was defined in terms of the principle of indifference , based on the natural symmetry of a problem, so, e.g. the probabilities of dice games arise from the natural symmetric 6-sidedness of the cube. (wikipedia.org)
• The simplest and oldest rule for determining a non-informative prior is the principle of indifference, which assigns equal probabilities to all possibilities. (wikipedia.org)
• describe
• First-excursion probabilities can be used to describe deflection to a critical point experienced by structures during "random loadings, such as earthquakes, strong gusts, hurricanes, etc. (wikipedia.org)
• random
• It is defined as an alternative probability measure conditioned on a particular value of a random variable . (wikipedia.org)
• Joseph Bertrand introduced it in his work Calcul des probabilités (1889) as an example to show that probabilities may not be well defined if the mechanism or method that produces the random variable is not clearly defined. (wikipedia.org)
• 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. (wikipedia.org)
• The relation of free probability with random matrices is a key reason for the wide use of free probability in other subjects. (wikipedia.org)
• A noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups. (wikipedia.org)
• Given a prefix-free Turing machine, the universality probability of it is the probability that it remains universal even when every input of it (as a binary string) is prefixed by a random binary string. (wikipedia.org)
• Although the universality probability of a Universal Turing Machine (UTM) was originally suspected to be zero, relatively simple proofs exist that the supremum of the set of universality probabilities is equal to 1, such as a proof based on random walks and a proof in Barmpalias and Dowe (2012). (wikipedia.org)
• Physical probabilities, which are also called objective or frequency probabilities, are associated with random physical systems such as roulette wheels, rolling dice and radioactive atoms. (wikipedia.org)
• In more technical terms, the probability distribution is a description of a random phenomenon in terms of the probabilities of events. (wikipedia.org)
• a multivariate distribution (a joint probability distribution) gives the probabilities of a random vector-a list of two or more random variables-taking on various combinations of values. (wikipedia.org)
• relative frequency
• The relative frequency of occurrence of an event, observed in a number of repetitions of the experiment, is a measure of the probability of that event. (wikipedia.org)
• They understand how to represent the theoretical probability for an event and can interpret the long-run relative frequency of an event. (ti.com)
• Students should notice that the more repetitions of an experiment leads to an relative frequency that is closer to the theoretical probability. (ti.com)
• likelihood
• Probability, which is the value assigned to the likelihood of an event occurring, can take on any numerical value between and including 0 and 1. (ti.com)
• This series of maps shows the probability (that is, the likelihood) that snowfall will equal or exceed specific amounts during the time period shown on the graphic. (weather.gov)
• interpretation
• Feller's comment was criticism of Laplace, who published a solution to the sunrise problem using an alternative probability interpretation. (wikipedia.org)
• In 1942, Paul Dirac wrote a paper "The Physical Interpretation of Quantum Mechanics" where he introduced the concept of negative energies and negative probabilities: "Negative energies and probabilities should not be considered as nonsense. (wikipedia.org)
• Laplace's
• Despite Laplace's explicit and immediate disclaimer in the source, based on expertise in astronomy as well as probability, two centuries of criticism have followed. (wikipedia.org)
• subjective
• Subjectivists assign numbers per subjective probability, i.e., as a degree of belief. (wikipedia.org)
• The expert knowledge is represented by some (subjective) prior probability distribution. (wikipedia.org)
• Imprecision is useful for dealing with expert elicitation, because: People have a limited ability to determine their own subjective probabilities and might find that they can only provide an interval. (wikipedia.org)
• formally
• More formally, it is the probability measure of reals (infinite binary sequences) which have the property that every initial segment of them preserves the universality of the given Turing machine. (wikipedia.org)
• theories
• The first formal treatment dates back at least to the middle of the nineteenth century, by George Boole, who aimed to reconcile the theories of logic (which can express complete ignorance) and probability. (wikipedia.org)
• example
• As it relates to insurance, underwriters may wish to know, for example, if both members of a married couple will reach the age of 75, given their independent probabilities. (investopedia.com)
• For example, using the default settings with a 20% probability increment 4arcs are displayed on the graph. (scottrade.com)
• 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. (wikipedia.org)
• for example, the probability of the event "the dice rolls an even value" is p ( 2 ) + p ( 4 ) + p ( 6 ) = 1 / 6 + 1 / 6 + 1 / 6 = 1 / 2. (wikipedia.org)
• For example, the probability that a given object weighs exactly 500 g is zero, because the probability of measuring exactly 500 g tends to zero as the accuracy of our measuring instruments increases. (wikipedia.org)
• belief
• On most accounts, evidential probabilities are considered to be degrees of belief, defined in terms of dispositions to gamble at certain odds. (wikipedia.org)
• rational
• Keynes's symbols allow expression of the general form of the probability relation represented by ex ante fundamental value, highlighting its dependence on unreliable propositions about future events, and also of the conventional basis of valuation, which it is only rational to adopt in such circumstances. (repec.org)
• However, when it is necessary to make a decision (such as deciding whether to place a bet), the behaviour of the rational person would suggest that the person has assigned a set of regular probabilities to the options. (wikipedia.org)
• The justification for the use of probability functions is usually linked to "rational" behavior to be held by an ideal agent involved in some decision contexts. (wikipedia.org)
• A re‐examination of probability matching and rational choice. (wikipedia.org)
• geometry
• Integral geometry sprang from the principle that the mathematically natural probability models are those that are invariant under certain transformation groups. (wikipedia.org)
• geometric
• Problems of the following type, and their solution techniques, were first studied in the 18th century, and the general topic became known as geometric probability. (wikipedia.org)
• Daniel A. Klain, Gian-Carlo Rota - Introduction to Geometric Probability. (wikipedia.org)
• Eugene Seneta, Karen Hunger Parshall, François Jongmans - Nineteenth-Century Developments in Geometric Probability: J. J. Sylvester, M. W. Crofton, J.-É. (wikipedia.org)
• given
• vanishingly small, but it has some probability of landing within a given area. (mcgill.ca)
• A)} What this means is that in describing an event, if all the information is given describing the event then the length of the information may be used to give the raw probability of the event. (wikipedia.org)