In probability theory, conditional independence describes situations wherein an observation is irrelevant or redundant when evaluating the certainty of a hypothesis. Conditional independence is usually formulated in terms of conditional probability, as a special case where the probability of the hypothesis given the uninformative observation is equal to the probability without. If is the hypothesis, and and are observations, conditional independence can be stated as an equality:
where is the probability of given both and . Since the probability of given is the same as the probability of given both and , this equality expresses that contributes nothing to the certainty of . In this case, and are said to be conditionally independent given , written symbolically as: . In the language of causal equality notation, two functions and which both depend on a common variable are described as conditionally independent using the notation , which is equivalent to the notation .
The concept of conditional independence is essential to graph-based theories of statistical inference, as it establishes a mathematical relation between a collection of conditional statements and a graphoid.
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In probability theory, conditionalindependence describes situations wherein an observation is irrelevant or redundant when evaluating the certainty of...
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption...
In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated...
dependent conditional on C . {\displaystyle C.} Conditionalindependence – Probability theory concept de Finetti's theorem – Conditionalindependence of exchangeable...
U+2AEB in Unicode) is a binary relation symbol used to represent: Conditionalindependence of random variables in probability theory Alternative plus sign...
{\displaystyle P(B)} and P ( A ∣ B ) {\displaystyle P(A\mid B)} . Such conditionalindependence relations can be represented with a Bayesian network or copula...
event Joint probability Marginal probability Conditional probability IndependenceConditionalindependence Law of total probability Law of large numbers...
number of events. Conditional probability is the probability of some event A, given the occurrence of some other event B. Conditional probability is written...
probability is a fundamental rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which...
event Joint probability Marginal probability Conditional probability IndependenceConditionalindependence Law of total probability Law of large numbers...
probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). While it is one of several...
event Joint probability Marginal probability Conditional probability IndependenceConditionalindependence Law of total probability Law of large numbers...
4 , {\displaystyle 1/4+1/2=3/4,} as in the diagram on the right. The conditional probability based on the intersection of events defined as: μ ( B ∣ A...
mathematical setsPages displaying short descriptions of redirect targets Conditional probability – Probability of an event occurring, given that another event...
algorithms. Maximum conditionalindependence: if the hypothesis can be cast in a Bayesian framework, try to maximize conditionalindependence. This is the bias...
((1/p1) − 1)/n + ((1/p2) − 1)/m. If X ~ B(n, p) and Y | X ~ B(X, q) (the conditional distribution of Y, given X), then Y is a simple binomial random variable...
event Joint probability Marginal probability Conditional probability IndependenceConditionalindependence Law of total probability Law of large numbers...
assumptions - conditionalindependence and conditional competence - are not justifiable simultaneously (under the same conditionalization). A possible...
definition of probability spaces gives rise to the natural concept of conditional probability. Every set A with non-zero probability (that is, P(A) > 0)...
{\displaystyle t} . Instead, the forward algorithm takes advantage of the conditionalindependence rules of the hidden Markov model (HMM) to perform the calculation...
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