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Simple English; Slovenščina ... the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the ...
This rule allows one to express a joint probability in terms of only conditional probabilities. [4] The rule is notably used in the context of discrete stochastic processes and in applications, e.g. the study of Bayesian networks, which describe a probability distribution in terms of conditional probabilities.
Every stationary chain can be proved to be time-homogeneous by Bayes' rule. A necessary and sufficient condition for a time-homogeneous Markov chain to be stationary is that the distribution of X 0 {\displaystyle X_{0}} is a stationary distribution of the Markov chain.
The logarithmic derivative is another way of stating the rule for differentiating the logarithm of a function (using the chain rule): () ′ = ′, wherever is positive. Logarithmic differentiation is a technique which uses logarithms and its differentiation rules to simplify certain expressions before actually applying the derivative.
The chain rule has a particularly elegant statement in terms of total derivatives. It says that, for two functions f {\displaystyle f} and g {\displaystyle g} , the total derivative of the composite function f ∘ g {\displaystyle f\circ g} at a {\displaystyle a} satisfies
As in the discrete case there is a chain rule for differential entropy: (|) = (,) [3]: 253 Notice however that this rule may not be true if the involved differential entropies do not exist or are infinite.
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In propositional logic, hypothetical syllogism is the name of a valid rule of inference (often abbreviated HS and sometimes also called the chain argument, chain rule, or the principle of transitivity of implication). The rule may be stated: