MCMC-based local parametric sensitivity estimations

Bayesian inferences for complex models need to be made by approximation techniques, mainly by Markov chain Monte Carlo (MCMC) methods. For these models, sensitivity analysis is a difficult task. A novel computationally low-cost approach to estimate local parametric sensitivities in Bayesian models is proposed. This method allows to estimate the sensitivity measures and their errors with the same random sample that has been generated to estimate the quantity of interest. Conditions to allow a derivative-integral interchange in the operator of interest are required. Two illustrative examples have been considered to show how sensitivity computations with respect to the prior distribution and the loss function are easily obtained in practice.