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{{Short description|Representations of imprecise probability}} ...method uses two numbers: the upper probability of the event and the lower probability of the event. ...

===[[Mathematical analysis|Analysis]]=== * [[Bernstein's inequality (mathematical analysis)]] ...

*[[Probability bounds analysis]], a mathematical method of risk analysis ...

{{Short description|Discrete probability distribution}} {{Probability distribution| ...

...ath>X</math> be a finite set and let <math>K(x,y)</math> be the transition probability for a reversible Markov chain on <math>X</math>. Assume this chain has [[st * {{cite book | last=Cheeger | first=Jeff | title=Problems in Analysis: A Symposium in Honor of Salomon Bochner (PMS-31) | chapter=A Lower Bound f ...

This is a '''list of probability topics'''. ...ns, see [[List of probability distributions]]. For journals, see [[list of probability journals]]. For contributors to the field, see [[list of mathematical proba ...

{{Short description|Concept in probability theory}} ...{{Cite journal |last=Huber |first=Mark |date=2019-11-26 |title=Halving the Bounds for the Markov, Chebyshev, and Chernoff Inequalities Using Smoothing |url=h ...

{{Short description|Inequality applying to probability spaces}} {{Probability fundamentals}} ...

...ing the number of standard deviations that correspond to the bounds of the probability band around the mean (<math>D_{\mathrm{max}}</math>) and comparing that val ...ervations, not <math>n-1</math> samples. In short, we are looking for the probability, <math>P</math>, that is equal to <math>n-\tfrac12</math> out of <math>n</m ...

{{Short description|Theorem in probability theory}} ...ntration inequality|concentration result]] for the values of [[martingale (probability theory)|martingale]]s that have bounded differences. ...

{{short description|Framework for mathematical analysis of machine learning}} ...tely correct''' ('''PAC''') '''learning''' is a framework for mathematical analysis of [[machine learning]]. It was proposed in 1984 by [[Leslie Valiant]].<ref ...

...als with how hard computations are, in quantitative terms, both with upper bounds ([[algorithm]]s whose complexity in the worst cases, as use of computing re *[[Halting probability]] ...

{{Short description|Similarity of two probability distributions}} ...ch represents a notion of [[similarity measure| similarity]] between two [[probability distribution]]s.<ref>{{Cite book |last=Dodge |first=Yadolah |url=https://bo ...

...ainty principle|quantum mechanics]], [[information theory]], and [[Fourier analysis]], the '''entropic uncertainty''' or '''Hirschman uncertainty''' is defined ...Beckner">{{Citation |first=W. |last=Beckner |title=Inequalities in Fourier analysis |journal=[[Annals of Mathematics]] |volume=102 |issue=6 |year=1975 |pages=1 ...

where <math>\rho(\vec{x},y)</math> is the unknown [[joint probability distribution]] for <math>\vec{x}</math> and <math>y</math>. Without knowing the joint probability distribution <math>\rho</math>, it is impossible to compute <math>I[f]</mat ...

...ess]]es such as [[Wiener process|Brownian motion]] and other [[Martingale (probability theory)|martingale]]s. Quadratic variation is just one kind of [[Total vari ...e that <math>X_t</math> is a real-valued stochastic process defined on a [[probability space]] <math>(\Omega,\mathcal{F},\mathbb{P})</math> and with time index <m ...

...lson made notable contributions to [[probability theory]] and [[functional analysis]]. These include: ...{{Cite journal|last=Wehner|first=Stephanie|date=2006-02-14|title=Tsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities|journal=[[Physical ...

{{Short description|Theorem in probability theory}} ...(mathematics)|normalized moment]]. It is also possible to give non-uniform bounds which become more strict for more extreme events. ...

..., and thus is [[dimensionless]], rather than having the same [[Dimensional analysis|dimension]] as the input values. Thus, the geometric standard deviation may data from a log-normally distributed population may be used to find the bounds of [[confidence interval]]s analogously to the way the arithmetic mean and ...

{{Short description|Exponentially decreasing bounds on tail distributions of random variables}} ...=Roman|url=https://www.worldcat.org/oclc/1029247498|title=High-dimensional probability : an introduction with applications in data science|date=2018|isbn=978-1-10 ...