Generic form of bayesian monte carlo for models with partial monotonicity

This paper presents a generic method for the safety assessments of models with partial monotonicity. For this purpose, a Bayesian interpolation method is developed and implemented in the Monte Carlo process. integrated approach is the generalization of the recently developed techniques used in safety assessment of monotonic models and it substantially increases the efficiency of Monte Carlo method. The formulation of this development is provided in this paper with an example showing its ability to dramatically improve efficiency of simulation. This is achieved by employing prior information obtained from monotonic models and outcomes of the preceding simulations. The theory and numerical algorithms of this method for multi-dimensional problems and their integration with the probabilistic finite element model of a real-world example are presented.