The paper presents a Bayesian framework for probabilistic sensitivity analysis of complex models, which is computationally efficient and allows for effective sensitivity analysis with fewer model runs compared to standard Monte Carlo methods. The approach unifies various tools of probabilistic sensitivity analysis and is particularly useful for expensive models where direct computation of outputs is time-consuming. The Bayesian method treats the model as an unknown function and uses a Gaussian process prior distribution to update it based on observed outputs. This allows for the estimation of main effects, interactions, variance-based sensitivity indices, and regression components, providing a deeper understanding of how inputs influence the model output. The paper also discusses the computation of these measures and provides examples to illustrate the methodology.The paper presents a Bayesian framework for probabilistic sensitivity analysis of complex models, which is computationally efficient and allows for effective sensitivity analysis with fewer model runs compared to standard Monte Carlo methods. The approach unifies various tools of probabilistic sensitivity analysis and is particularly useful for expensive models where direct computation of outputs is time-consuming. The Bayesian method treats the model as an unknown function and uses a Gaussian process prior distribution to update it based on observed outputs. This allows for the estimation of main effects, interactions, variance-based sensitivity indices, and regression components, providing a deeper understanding of how inputs influence the model output. The paper also discusses the computation of these measures and provides examples to illustrate the methodology.