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S0, df0, R2 (numeric) define the prior assigned to the residual variance, df0 defines the degrees of freedom, and S0 defines the scale.
The prior assigned to parameters enters into the evidence calculation and can influence the outcome of model comparison through the evidence (or Bayes factor) [ 26].
This assumption can be justified based on "ignorance"; however, in many instances we may have additional prior information about markers and we may want to incorporate such information into the prior assigned to marker effects.
Bayes B uses a mixture distribution with a mass at zero, such that the (conditional) prior distribution of marker effects is given by The prior assigned to σ j 2, j = 1, …., p is the same for all markers, i.e. a scaled inverted chi squared distribution χ − 2 (d f β, s β ), where d f β are the degrees of freedom and s β is a scaling parameter.
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However, this does not directly occur when the priors assigned to marker effects are from the thick-tailed family.
The general idea of so-called Jeffreys priors is that the prior probability assigned to a small patch in the parameter space is proportional to, what may be called, the density of the distributions within that patch.
A Bernoulli prior was assigned to r j: P (r j | w ) = w r j (1 − w ) r j.
We treat most of these regularization parameters as random; consequently a prior is assigned to these unknowns.
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