AC-130 gunship video.

For non-statisticians in the audience, Type I error is incorrect rejection of the null hypothesis (false positive) and Type II error is failure to reject a false null hypothesis (false negative).

The Fire Control Officer has rejected the null hypothesis.

In this particular instance, I imagine Type I error is more of a concern for people on the ground and people in the air are seeking to keep Type II error below a particular threshold.  In general, decision processes seek to balance Type I error against Type II error – less Type I means more Type II, less Type II means more Type I.    Where you set your decision threshold depends upon how you weight the significance of Type I and Type II errors.  Or, conversely, by setting a decision threshold you’ve made a declaration about the relative importance you place on Type I and Type II errors.

[More to come on minimization of Bayes risk.]