# eplogprob - Compute approximate marginal inclusion probabilities from pvalues

### Description

`eplogprob`

calculates approximate marginal posterior
inclusion probabilities from p-values computed from a linear model
using a lower bound approximation to Bayes factors. Used to obtain
initial inclusion probabilities for sampling using Bayesian Adaptive
Sampling `bas.lm`

### Usage

1 |

### Arguments

`lm.obj` |
a linear model object |

`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 |

`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`

.

### Value

`eplogprob`

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.
If the model is not full rank, variables that are linearly dependent
base on the QR factorization will have NA for their p-values. In
bas.lm, where the probabilities are used for sampling, the inclusion
probability is set to 0.

### 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.

### See Also

`bas`

### Examples

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