In orthodox probability theory, only certain trivial Boolean algebras with very few elements contain, for any given A and B, an event X which satisfies P(X) = P(B|A). Later extended by others, this result stands as a major obstacle to any talk about logical objects that can be the bearers of conditional probabilities.I'm aware that in Bayesian analysis, the conditional likelihood P(B|A) is not a probability distribution. There must be a connection here right? What are some simple examples of conditional events that are not in the event algebra?

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In orthodox probability theory, only certain trivial Boolean algebras with very few elements contain, for any given A and B, an event X which satisfies P(X) = P(B|A). Later extended by others, this result stands as a major obstacle to any talk about logical objects that can be the bearers of conditional probabilities.I&#039;m aware that in Bayesian analysis, the conditional likelihood P(B|A) is not a probability distribution. There must be a connection here right? What are some simple examples of conditional events that are not in the event algebra?

Jerry Kidd · Accepted Answer

&quot;in orthodox probability theory, only certain trivial Boolean algebras with very few elements contain, for any given A and B, an event X which satisfies P(X) = P(B|A).&quot;On   (  Ω  ,  F  ,  P  )  =  (  [  0  ,  1  ]  ,  B  (  [  0  ,  1  ]  )  ,      L    e    b    ), for every   A and   B, there exists an event   X such that   P  (  X  )  =  P  (  B  ∣  A  ) (as soon as the RHS exists): pick   X  =  [  0  ,  x  ] where   x  =  P  (  B  ∣  A  ).&quot;...in Bayesian analysis, the conditional likelihood P(B|A) is not a probability distribution...&quot;When it exists, the mapping   P  (     ∣  A  ) is very much a probability measure.&quot;What are some simple examples of conditional events that are not in the event algebra?&quot;Define &quot;conditional event&quot;.

In orthodox probability theory, only certain trivial Boolean algebras with very few elements contain

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