Say I have a binary outcome of 0 or 1 and suppose I were to use logistic regression model to estimate the probability a new sample will have an outcome of 1.
I have read answers (for example here: Computing prediction intervals for logistic regression) that indicate it's nonsensical to compute prediction intervals, as the outcome can only be 0 or 1.
However, is there nevertheless a sensible way to compute a prediction interval in log-odds space, before transforming it using the logistic function into a probability interval?
My goal is to be able to communicate a level of uncertainty in each new prediction I make (e.g,. "This new product is estimated at a 0.40 probability of having the desired outcome, but the prediction interval around this estimate is [0.3, 0.5]").