Is there a difference in the meanings of stochastic and aleatory? Are these words interchangeable? So far I have not been able to find a meaningful difference.

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    $\begingroup$ A process can be stochastic...a variable can be random or aleatory. See this question for a related discussion. $\endgroup$ – lulu Oct 5 '16 at 21:15
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    $\begingroup$ The word aleatory (translation from French "aléatoire" ?) is uncommon in english. "Random" should be used instead. $\endgroup$ – Jean Marie Oct 5 '16 at 21:18

Aleatory is a subset of stochastic. A stochastic process is aleatoric or epistemic. If it is aleatoric, the uncertainty inherently cannot be reduced. If it is epistemic, then cleverly adding data can reduce the uncertainty.

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