This model implies that X and Z are unconditionally independent, and that there are no further non-trivial conditional or unconditional independence relations.
All three imply that Y screens X off from Z, and that there are no further non-trivial relations of conditional or unconditional independence.
One is trivial, essentially asserting that a conditional frequency on lags (Reichenbach's term for lags is "phases") of a constant "variable" can always be replaced by a conditional frequency on no lag of that variable.
(The conditional is a condition.
For example, there is not any non-trivial proposition N which could turn the conditional "normally a Cs137 atom decays after 60 years" into a strict implication of the form "if N, then a Cs137 atom decays after 60 years".
Pivotal to its success is the efficient generation of conditional failure samples, which is generally non-trivial.
Conditional bimodality is an unexpected and non-trivial property of gene expression.
For the models that excluded maternal height, inclusion of the India cohort altered the estimates by only trivial amounts, and in models that included length at 12 mo and conditional heights at 24 mo and mid-childhood, addition of the Brazil and South Africa samples resulted in trivial changes to the estimates.
Consequently, it made no sense to nest this conditionals within disjunctions (as though the agent couldn't tell which disjunct represented his actual probability assignment) or within other conditionals (since the subjective probability of a subjective probability is always trivial — either exactly 1 or exactly 0).
The conditional probability method, which was first published in an informatics journal, is not trivial and probably not easy to understand for many medicinal chemists.
To address this, an extension of CBPK, referred to herein as extended conditional bias penalized kriging (ECBPK), has been developed which combines the CBPK estimate with a trivial estimate of zero precipitation.
