Probability estimates are not the same thing as uncertainty.
Consider tossing a coin. If I see 2 heads and 2 tails, I might report "the probability of heads is 50%". If you see 2000 heads and 2000 tails you'd also report the SAME probability estimate -- but you'd be more certain than me.
Neural networks give probability estimates. Bayesian methods (and also frequentist methods) give us probability estimates AND uncertainty.
The literature on neural network calibration seems to me to have missed this distinction.
Consider tossing a coin. If I see 2 heads and 2 tails, I might report "the probability of heads is 50%". If you see 2000 heads and 2000 tails you'd also report the SAME probability estimate -- but you'd be more certain than me.
Neural networks give probability estimates. Bayesian methods (and also frequentist methods) give us probability estimates AND uncertainty.
The literature on neural network calibration seems to me to have missed this distinction.