Since these correlations remain conditional on the full prior state (S1), there can be no quantity such that conditional upon a prior value of this quantity A and B are uncorrelated.
The approach is reminiscent of the probability field simulation, which also maps the conductivity realizations onto a field of uniform random numbers; although the mapping now is done using the local conditional distribution functions built based on a prior statistical model and the conditioning data.
We will employ 2 analytical approaches in these analyses: (1) ITT based on the original randomized design and examining each intermediate outcome separately as an endpoint; and (2) per-protocol analyses linking together intermediate steps and conditional on specific prior outcomes or achievements in an earlier step, such as high FOI.
Each split is determined in a data driven way, with lower splits all conditional on the prior splits.
This parameterization implies that individual variances for each SNP (i.e. τi) are estimated, conditional on a regularization parameter λ, which was estimated by using a prior gamma distribution bounded between 0 and 10.
Conditional on prior high school performance, we find that students participating in Running Start are more likely to attend any college but less likely to attend four-year colleges in the year after high school graduation.
However, in practice, the use of ratio methods is conditional on prior knowledge of both (i) significant changes in TSPO expression in target regions such that interregional correlations are reduced and (ii) significant equivalence [11, 12] of TSPO expression in the reference region between groups.
In brief, it involves parametric models for the outcome and all time-varying covariates and exposures, conditional on prior exposure and covariate histories as well as baseline covariates.
Fortunately, this prior can also be specified as a normally distributed marker effect conditional on a locus-specific variance, which is given a scaled inverted chi-square distribution.
This suggestion is sensitive to the well-recognized fact that we are not always able to assign a prior to every hypothesis of interest, or to say how probable a given piece of evidence is conditional on a given hypothesis.
