Revealing priors from posteriors with an application to inflation forecasting in the UK

A Bayesian typically uses data and a prior to produce a posterior. We shall follow the opposite route, using data and the posterior information to reveal the prior. We then apply this theory to inflation forecasts by the Bank of England and the National Institute of Economic and Social Research in an attempt to get some insight into the prior beliefs of the policy makers in these two institutions, especially under the uncertainties about the Brexit referendum, the Covid-19 lockdown, and the Russian invasion of Ukraine.