Probabilistic Risk Analysis

As Bayesians, we try to acknowledge all our uncertainties about data and models and express them as probability distributions. As we have seen, this approach allows us to quantify predictive uncertainty when we use our models for prediction. And this is of course important for the user of these predictions, whether that user is us or someone to whom we report our results. Our probabilistic predictions allow calculation of risks and, more generally, provide support for decision-making. This chapter introduces a rigorous method of probabilistic risk analysis (PRA), and the next chapter broadens the perspective to Bayesian decision theory (BDT). The two chapters summarise new theory for PRA and its links to BDT that was presented in greater detail by Van Oijen and Brewer (Probabilistic risk analysis and Bayesian decision theory. SpringerBriefs in Statistics. Springer International Publishing, 2022).