7. Error propagation

In Bayesian statistics, error propagation is the process of determining how uncertainties in input parameters, which are characterized by probability distributions, influence the uncertainty (again, as a PDF) in the final output of a model. In general, Bayesian methods use the full PDFs to propagate uncertainty, in contrast to frequentist approaches. In this chapter we look at three aspects of error propagation plus solutions to exercises:

• Error propagation (I): Nuisance parameters and marginalization

• Error propagation (II): Changing variables

• Error propagation (III): A useful approximation

• Solutions