Before revision:  In this work we show that exact Bayesian inference gives naturally rise to a surprise-modulated trade-off between URLetting and integrating the new observations with the current belief.
After revision:  In this work we show that exact Bayesian inference gives naturally rise to a surprise-modulated trade-off between URLetting old observations and integrating them with the new ones. The modulation depends on a probability ratio, called the "Bayes Factor Surprise" that tests the prior belief against the current belief.