where F w (•) is the output of BNN model F with weight setting w. Under a heteroscedastic model, the the BNN output with configuration w t is (ŷ * t , σt ) = F wt (x * ), where the t th Monte Carlo weight sample is drawn from q θ (w). After T such Monte Carlo samples, the total heteroscedastic predictive uncertainty is given by the following expression, which can be divided into contributions from epistemic and aleatoric uncertainties.