So, upon learning that my calculations were wrong, am I correct in saying that my new probability estimate—before doing any further calculations—should become whatever my prior probability was before I did the calculation?
Let me be more precise: before you see anything wrong with your calculations, you have no real reason to expect locating an error in them to give you evidence of anything specific. Therefore, when doing your initial post-calculations, the prior probability is appropriate.
After you find an error in your calculations, you can usually fix the error in your calculations.
Not quite. It depends on your beliefs about how the calculation could go wrong and how much this would change the result. If you are very confident in all parts except a minor correcting term, and are simply told that there is an error in the calculation, then you can still have some kind of rough confidence in the result (you can see how to spell this out in maths). If you know the exact part of the calculation that was mistaken, then the situation is slightly different, but still not identical to reverting to your prior.
So, upon learning that my calculations were wrong, am I correct in saying that my new probability estimate—before doing any further calculations—should become whatever my prior probability was before I did the calculation?
Let me be more precise: before you see anything wrong with your calculations, you have no real reason to expect locating an error in them to give you evidence of anything specific. Therefore, when doing your initial post-calculations, the prior probability is appropriate.
After you find an error in your calculations, you can usually fix the error in your calculations.
Not quite. It depends on your beliefs about how the calculation could go wrong and how much this would change the result. If you are very confident in all parts except a minor correcting term, and are simply told that there is an error in the calculation, then you can still have some kind of rough confidence in the result (you can see how to spell this out in maths). If you know the exact part of the calculation that was mistaken, then the situation is slightly different, but still not identical to reverting to your prior.