With priors of 1 or 0, Bayes rule stops working permanently. If something is running on real hardware, then it has a limit on its numeric precision. On a system that was never designed to make precise mathematical calculations, one where 8⁄10 doesn’t feel significantly different from 9⁄10, or one where “90% chance” feels like “basically guaranteed”, the level of numeric precision may be exceedingly low, such that it doesn’t even take a lot for a level of certainty to be either rounded up to one or rounded down to 0.
With priors of 1 or 0, Bayes rule stops working permanently. If something is running on real hardware, then it has a limit on its numeric precision. On a system that was never designed to make precise mathematical calculations, one where 8⁄10 doesn’t feel significantly different from 9⁄10, or one where “90% chance” feels like “basically guaranteed”, the level of numeric precision may be exceedingly low, such that it doesn’t even take a lot for a level of certainty to be either rounded up to one or rounded down to 0.
As always, thanks for the post!