Bayesian local influence analysis: With an application to stochastic frontiers

A Bayesian alternative to Zhuo (2018) is presented. The method is of general interest as it presents an explicit formula for the local sensitivity of log marginal likelihood when observations vary by a small amount. The remarkable feature is that the formula is very easy to compute and does not require knowledge of the marginal likelihood which is, invariably, extremely difficult to compute. Similar expressions are derived for posterior moments and other functions of interest, including inefficiency. Methods for examining prior sensitivity in a straightforward way are also presented. The methods are illustrated in the context of a stochastic production frontier.