# eplogprob-marg: eplogprob.marg - Compute approximate marginal inclusion...

### Description

`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 `bas.lm`

### Usage

 `1` ```eplogprob.marg(Y, X, thresh=.5, max = 0.99, int=TRUE) ```

### Arguments

 `Y` response variable `X` design matrix with a column of ones for the intercept `thresh` the value of the inclusion probability when if the p-value > 1/exp(1), where the lower bound approximation is not valid. `max` maximum value of the inclusion probability; used for the `bas.lm` function to keep initial inclusion probabilities away from 1. `int` If the Intercept is included in the linear model, set the marginal inclusion probability corresponding to the intercept to 1

### Details

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 `thresh`. 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.

### Value

`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.

### Author(s)

Merlise Clyde clyde@stat.duke.edu

### References

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.

`bas`

### Examples

 ```1 2 3 4``` ```library(MASS) data(UScrime) UScrime[,-2] = log(UScrime[,-2]) eplogprob(lm(y ~ ., data=UScrime)) ```

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