Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two events are independent, statistically...

In probability theory, conditional independence describes situations wherein an observation is irrelevant or redundant when evaluating the certainty of...

In probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are independent. Any collection...

Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations...

In probability theory and statistics, a collection of random variables is independent and identically distributed (i.i.d., iid, or IID) if each random...

total probability Bayes' theorem Independence (probability theory) (Related topics: measure theory) Sample spaces, σ-algebras and probability measures...

Free probability is a mathematical theory that studies non-commutative random variables. The "freeness" or free independence property is the analogue...

The standard probability axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain...

In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It...

In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each...

In statistics, there is a negative relationship or inverse relationship between two variables if higher values of one variable tend to be associated with...

vine is a graphical tool for labeling constraints in high-dimensional probability distributions. A regular vine is a special case for which all constraints...

computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe...

In statistics and social sciences, an antecedent variable is a variable that cannot help to explain the apparent relationship (or part of the relationship)...

In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. A single outcome...

In probability theory and related fields, a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random...

Causal inference, Chapman & Hall/CRC monographs on statistics & applied probability, CRC, p. 70, ISBN 978-1-4200-7616-5 Julia M. Rohrer (2018-07-02). "Thinking...

(mathematical logic), logical independence Independence (probability theory), statistical independence Linear independence Independence (1976 film), a docudrama...

In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption...

In statistics, a spurious relationship or spurious correlation is a mathematical relationship in which two or more events or variables are associated but...

between the two corresponding probabilities, conditional on the X values not being equal. If X has a continuous probability distribution, then τ ( X , X...

In probability theory, a tree diagram may be used to represent a probability space. A tree diagram may represent a series of independent events (such...

possibilities, we find x 1 x 2 = { + 1  with probability  N + ( N + − 1 ) + N − ( N − − 1 ) N ( N − 1 ) − 1  with probability  2 N + N − N ( N − 1 ) {\displaystyle...

In probability theory, a random variable Y {\displaystyle Y} is said to be mean independent of random variable X {\displaystyle X} if and only if its conditional...

In probability theory, a probability space or a probability triple ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},P)} is a mathematical construct...

information theory, algorithmic probability, also known as Solomonoff probability, is a mathematical method of assigning a prior probability to a given...

influence each other. Through propagation of independence, the independence of Ui implies independence of Yi, even though each Yi has a different expectation...

(1995). Probability and Measure. John Wiley. ISBN 0-471-00710-2. Ash, Robert B.; Doléans-Dade, Catherine A. (1999). Probability & Measure Theory. Academic...

statistics, Local independence is the underlying assumption of latent variable models (such as factor analysis and item response theory models). The observed...

"Transport Catastrophe Analysis as an Alternative to a Monofractal Description: Theory and Application to Financial Crisis Time Series". Journal of Chaos. 2014:...