Editing Conditional independence (section)

==Uses in Bayesian inference==
Let ''p'' be the proportion of voters who will vote "yes" in an upcoming [[referendum]]. In taking an [[opinion poll]], one chooses ''n'' voters randomly from the population. For ''i''&nbsp;=&nbsp;1,&nbsp;...,&nbsp;''n'', let ''X''<sub>''i''</sub>&nbsp;=&nbsp;1 or 0 corresponding, respectively, to whether or not the ''i''th chosen voter will or will not vote "yes".

In a [[frequency probability|frequentist]] approach to [[statistical inference]] one would not attribute any probability distribution to ''p'' (unless the probabilities could be somehow interpreted as relative frequencies of occurrence of some event or as proportions of some population) and one would say that ''X''<sub>1</sub>, ..., ''X''<sub>''n''</sub> are [[statistical independence|independent]] random variables.

By contrast, in a [[Bayesian inference|Bayesian]] approach to statistical inference, one would assign a [[probability distribution]] to ''p'' regardless of the non-existence of any such "frequency" interpretation, and one would construe the probabilities as degrees of belief that ''p'' is in any interval to which a probability is assigned. In that model, the random variables ''X''<sub>1</sub>,&nbsp;...,&nbsp;''X''<sub>''n''</sub> are ''not'' independent, but they are '''conditionally independent''' given the value of ''p''. In particular, if a large number of the ''X''s are observed to be equal to 1, that would imply a high [[conditional probability]], given that observation, that ''p'' is near 1, and thus a high [[conditional probability]], given that observation, that the ''next'' ''X'' to be observed will be equal to 1.