Compute calibrated p-values that can be interpreted probabilistically, i.e. as posterior probability of H0 (given that H0 and H1 have equal prior probabilities).

## Usage

```
p_calibrate(x, ...)
# Default S3 method
p_calibrate(x, type = "frequentist", verbose = TRUE, ...)
```

## Details

The Bayesian calibration, i.e. when `type = "bayesian"`

, can be interpreted
as the lower bound of the Bayes factor for H0 to H1, based on the data.
The full Bayes factor would then require multiplying by the prior odds of
H0 to H1. The frequentist calibration also has a Bayesian interpretation; it
is the posterior probability of H0, assuming that H0 and H1 have equal
prior probabilities of 0.5 each (*Sellke et al. 2001*).

The calibration only works for p-values lower than or equal to `1/e`

.

## References

Thomas Sellke, M. J Bayarri and James O Berger (2001) Calibration of p Values for Testing Precise Null Hypotheses, The American Statistician, 55:1, 62-71, doi:10.1198/000313001300339950

## Examples

```
model <- lm(mpg ~ wt + as.factor(gear) + am, data = mtcars)
p_calibrate(model, verbose = FALSE)
#> Parameter | p | p (calibrated)
#> ------------------------------------------
#> (Intercept) | < .001 | < .001
#> wt | < .001 | < .001
#> as.factor(gear)4 | 0.242 | 0.483
#> as.factor(gear)5 | 0.660 |
#> am | 0.925 |
#> Calibrated p-values indicate the posterior probability of H0.
#>
```