eplogprob.marg calculates approximate marginal posterior
inclusion probabilities from p-values computed from a series of simple
linear regression models using a lower bound approximation to Bayes
factors. Used to order variables and if appropriate obtain initial
inclusion probabilities for sampling using Bayesian Adaptive Sampling
design matrix with a column of ones for the intercept
the value of the inclusion probability when if the p-value > 1/exp(1), where the lower bound approximation is not valid.
maximum value of the inclusion probability; used for
If the Intercept is included in the linear model, set the marginal inclusion probability corresponding to the intercept to 1
Sellke, Bayarri and Berger (2001) provide a simple calibration of p-values
BF(p) = -e p log(p)
which provide a lower bound to a Bayes factor for comparing H0: beta = 0 versus H1: beta not equal to 0, when the p-value p is less than 1/e. Using equal prior odds on the hypotheses H0 and H1, the approximate marginal posterior inclusion probability
p(beta != 0 | data ) = 1/(1 + BF(p))
When p > 1/e, we set the marginal inclusion probability to 0.5 or the
value given by
For the eplogprob.marg the marginal p-values are obtained using
statistics from the p simple linear regressions
P(F > (n-2) R2/(1 - R2)) where F ~ F(1, n-2) where R2 is the square of the correlation coefficient between y and X_j.
eplogprob.prob returns a vector of marginal posterior inclusion
probabilities for each of the variables in the linear model. If int =
TRUE, then the inclusion probability for the intercept is set to 1.
Merlise Clyde email@example.com
Sellke, Thomas, Bayarri, M. J., and Berger, James O. (2001), “Calibration of p-values for testing precise null hypotheses”, The American Statistician, 55, 62-71.
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