  The problem of Voodoo correlations is recognized in neuroimaging as the
problem of estimating quantities of interest from the same data that was used
to select them as interesting. In statistical terminology, the problem of
inference following selection from the same data is that of selective
inference. Motivated by the unwelcome side-effects of the recommended remedy-
splitting the data. A method for constructing confidence intervals based on the
correct post-selection distribution of the observations has been suggested
recently. We utilize a similar approach in order to provide point estimates
that account for a large part of the selection bias. We show via extensive
simulations that the proposed estimator has favorable properties, namely, that
it is likely to reduce estimation bias and the mean squared error compared to
the direct estimator without sacrificing power to detect non-zero correlation
as in the case of the data splitting approach. We show that both point
estimates and confidence intervals are needed in order to get a full assessment
of the uncertainty in the point estimates as both are integrated into the
Confidence Calibration Plots proposed recently.
  The computation of the estimators is implemented in an accompanying software
package.
