This paper presents a Bayesian framework for probabilistic sensitivity analysis of complex models. The authors propose a unified approach that allows efficient sensitivity analysis of expensive models, which are those that require many computational resources to evaluate. The framework is based on treating the model as an unknown function and using a Gaussian process prior to model uncertainty in the inputs. This approach enables the estimation of various sensitivity measures, including main effects, interactions, and variance-based indices, from a single set of model runs. The paper discusses the importance of sensitivity analysis in understanding how changes in model inputs influence outputs. It highlights the limitations of traditional methods, such as Monte Carlo simulations, which are often impractical for expensive models. The Bayesian approach is computationally efficient and allows for the estimation of sensitivity measures with fewer model runs. The authors introduce a variety of sensitivity measures, including main effects, total effects, and variance-based indices. These measures are derived from the decomposition of the model output into components that reflect the influence of individual inputs and their interactions. The Bayesian framework allows for the estimation of these measures using a Gaussian process prior, which accounts for uncertainty in the model inputs. The paper also discusses the use of regression components in sensitivity analysis, where the model output is approximated by a linear function of the inputs. The authors show that the Bayesian approach can be used to estimate the variance of the model output and the variance explained by the regression approximation. The authors present two examples to illustrate the application of their methodology. The first example is a synthetic model, where the model output is a combination of linear and nonlinear terms. The second example is a real-world model, where the model output is a function of multiple inputs. The results show that the Bayesian approach is effective in estimating sensitivity measures for both types of models. In conclusion, the paper presents a Bayesian framework for probabilistic sensitivity analysis of complex models. The framework allows for the efficient estimation of sensitivity measures, including main effects, interactions, and variance-based indices, from a single set of model runs. The approach is particularly useful for expensive models, where traditional methods are impractical. The Bayesian framework provides a unified approach that can be applied to a wide range of models and is computationally efficient.This paper presents a Bayesian framework for probabilistic sensitivity analysis of complex models. The authors propose a unified approach that allows efficient sensitivity analysis of expensive models, which are those that require many computational resources to evaluate. The framework is based on treating the model as an unknown function and using a Gaussian process prior to model uncertainty in the inputs. This approach enables the estimation of various sensitivity measures, including main effects, interactions, and variance-based indices, from a single set of model runs. The paper discusses the importance of sensitivity analysis in understanding how changes in model inputs influence outputs. It highlights the limitations of traditional methods, such as Monte Carlo simulations, which are often impractical for expensive models. The Bayesian approach is computationally efficient and allows for the estimation of sensitivity measures with fewer model runs. The authors introduce a variety of sensitivity measures, including main effects, total effects, and variance-based indices. These measures are derived from the decomposition of the model output into components that reflect the influence of individual inputs and their interactions. The Bayesian framework allows for the estimation of these measures using a Gaussian process prior, which accounts for uncertainty in the model inputs. The paper also discusses the use of regression components in sensitivity analysis, where the model output is approximated by a linear function of the inputs. The authors show that the Bayesian approach can be used to estimate the variance of the model output and the variance explained by the regression approximation. The authors present two examples to illustrate the application of their methodology. The first example is a synthetic model, where the model output is a combination of linear and nonlinear terms. The second example is a real-world model, where the model output is a function of multiple inputs. The results show that the Bayesian approach is effective in estimating sensitivity measures for both types of models. In conclusion, the paper presents a Bayesian framework for probabilistic sensitivity analysis of complex models. The framework allows for the efficient estimation of sensitivity measures, including main effects, interactions, and variance-based indices, from a single set of model runs. The approach is particularly useful for expensive models, where traditional methods are impractical. The Bayesian framework provides a unified approach that can be applied to a wide range of models and is computationally efficient.