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###### Decision analysis
B. Fischhoff; L. D. Phillips & S. Lichtenstein (1982). "Calibration of Probabilities: The State of the Art to 1980". In D. ... Uncertainties are represented through probabilities. The decision maker's attitude to risk is represented by utility functions ... or which maximize the probability of achieving the uncertain aspiration level). Such decision analytic methods are used in a ... utility functions can be replaced by the probability of achieving uncertain aspiration levels. Decision analysis advocates ...
###### Log-Cauchy distribution
In probability theory, a log-Cauchy distribution is a probability distribution of a random variable whose logarithm is ... The log-Cauchy distribution has the probability density function: f ( x ; μ , σ ) = 1 x π σ [ 1 + ( ln ⁡ x − μ σ ) 2 ] , x > 0 ... Good, I.J. (1983). Good thinking: the foundations of probability and its applications. University of Minnesota Press. p. 102. ... the probability density function reduces to: f ( x ; 0 , 1 ) = 1 x π ( 1 + ( ln ⁡ x ) 2 ) , x > 0 {\displaystyle f(x;0,1)={\ ...
###### Regular conditional probability
See also conditional probability and conditional probability distribution. Consider a Radon space Ω {\displaystyle \Omega } ( ... "transition probability", where ν ( x , A ) {\displaystyle \nu (x,A)} is a valid probability measure (in its second argument) on ... is said to have the regular conditional probability property if for all probability measures P {\displaystyle P} on ( Ω , F ... This limit is defined if and only if the probability space is Radon, and only in the support of T, as described in the article ...
###### Polish space
Since a probability measure is globally finite, and hence a locally finite measure, every probability measure on a Radon space ... A Radon space, named after Johann Radon, is a topological space such that every Borel probability measure on M is inner regular ... Ambrosio, L., Gigli, N. & Savaré, G. (2005). Gradient Flows in Metric Spaces and in the Space of Probability Measures. Basel: ... Polish spaces are also a convenient setting for more advanced measure theory, in particular in probability theory. Common ...
###### Probability
... is the measure of the likelihood that an event will occur. See glossary of probability and statistics. Probability ... of Ala.-Huntsville) Probability on In Our Time at the BBC. Probability and Statistics EBook Edwin Thompson Jaynes. Probability ... Conditional probability is the probability of some event A, given the occurrence of some other event B. Conditional probability ... The most popular version of objective probability is frequentist probability, which claims that the probability of a random ...
###### Geometric probability
Daniel A. Klain, Gian-Carlo Rota - Introduction to Geometric Probability. Maurice G. Kendall, Patrick A. P. Moran - Geometrical ... Integral geometry sprang from the principle that the mathematically natural probability models are those that are invariant ... Eugene Seneta, Karen Hunger Parshall, François Jongmans - Nineteenth-Century Developments in Geometric Probability: J. J. ... Wendel's theorem Herbert Solomon (1978). Geometric Probability. Philadelphia, PA: Society for Industrial and Applied ...
###### Negative probability
Similarly he argued how negative probabilities as well as probabilities above unity possibly could be useful in probability ... In quantitative finance most probabilities are not real probabilities but pseudo probabilities, often what is known as risk ... In terms of extended probability, a negative value (say, −0.1) of the probability for the word "texxt" to appear in his text T ... turns out to be what Feynman and others referred to as "quasi-probability." Note that when a quasi-probability is larger than 1 ...
###### Probability Sun
... is a 2001 science fiction novel by American writer Nancy Kress, a sequel to her 2000 publication Probability ... "PROBABILITY SUN by Nancy Kress". Kirkus Reviews. 2001-04-15. Retrieved 2015-07-11. "Probability Sun". Publishers Weekly. ... The Probability trilogy takes place in a galaxy that has been colonized by humans. This was made possible by the space tunnels ... The Probability novels shares two technological quirks with another of Nancy Kress' trilogies, the Beggars trilogy: in both ...
###### Coupling (probability)
Assume two biased coins, the first with probability p of turning up heads and the second with probability q > p of turning up ... 1 with probability (q-p)/(1-p). Then the sequence of Yi has exactly the probability distribution of tosses made with the second ... the probability that the first coin produces at least k heads should be less than the probability that the second coin produces ... In probability theory, coupling is a proof technique that allows one to compare two unrelated random variables(distributions) X ...
###### Prior probability
Similarly, the prior probability of a random event or an uncertain proposition is the unconditional probability that is ... Some attempts have been made at finding a priori probabilities, i.e. probability distributions in some sense logically required ... in the case of probability distributions, is the negative expected value of the logarithm of the probability mass or density ... For example, the maximum entropy prior on a discrete space, given only that the probability is normalized to 1, is the prior ...
###### Excursion probability
In probability theory, an excursion probability is the probability that a stochastic process surpasses a given value in a fixed ... It is the probability P { sup t ∈ T f ( t ) ≥ u } . {\displaystyle \mathbb {P} \left\{\sup _{t\in T}f(t)\geq u\right\}.} ... First-excursion probabilities can be used to describe deflection to a critical point experienced by structures during "random ... Yang, J. -N. (1973). "First-excursion probability in non-stationary random vibration". Journal of Sound and Vibration. 27 (2): ...
###### Free probability
The relation of free probability with random matrices is a key reason for the wide use of free probability in other subjects. ... RMTool - A MATLAB-based free probability calculator. Alcatel-Lucent Chair on Flexible Radio Applications of Free Probability to ... Free probability is currently undergoing active research. Typically the random variables lie in a unital algebra A such as a C- ... Free probability is a mathematical theory that studies non-commutative random variables. The "freeness" or free independence ...
###### Log probability
... a log probability is simply the logarithm of a probability. The use of log probabilities means representing probabilities in ... probabilities. Accuracy. The use of log probabilities improves numerical stability, when the probabilities are very small, ... The logarithm function is not defined for zero, so log probabilities can only represent non-zero probabilities. Since the ... However, in many applications a multiplication of probabilities (giving the probability of all independent events occurring) is ...
###### Universality probability
Universality probabilities are very related to the Chaitin constant, which is the halting probability of a universal prefix- ... In particular, the universality probability can be seen as the non-halting probability of a machine with oracle the third ... the universality probability of it is the probability that it remains universal even when every input of it (as a binary string ... the non-halting probability of any prefix-free machine with this highly non-computable oracle is the universality probability ...
###### Probability distribution
The probability density function describes the infinitesimal probability of any given value, and the probability that the ... Probability density, Probability density function, p.d.f., Continuous probability distribution function: most often reserved ... A discrete probability distribution is a probability distribution characterized by a probability mass function. Thus, the ... Because a probability distribution P on the real line is determined by the probability of a scalar random variable X being in a ...