1. A simulating machine for simulating a stochastic system characterized by a system output defined by a set of system components influenced by a set of system parameters (θ) defining a system model, the simulating machine comprising: a processor; a memory coupled to said processor; a sample generator, coupled to said processor and said memory, configured to provide samples of said set of system components influenced by said set of system parameters (θ); and a differentiator coupled to said sample generator, said differentiator configured to operate on said samples in accordance with adjoint algorithm differentiation to provide a first sensitivity (dP/dθ) of said system output (P) with respect to at least one of said set of system parameters (θ) for each of a plurality of scenarios under simulation, and a second sensitivity (dV/dθ) of an expected value (V) of the system output with respect to at least one of said system parameters across the plurality of scenarios under simulation, wherein the second sensitivity and the expected value are based on the following formulation: V MC = 1 N scenarios ⁢ ∑ i ⁢ ⁢ scenario = 1 N scenarios ⁢ P ⁡ ( X ⁡ [ i ⁢ ⁢ scenario ] , θ ) ∂ V ∂ θ i = 1 N scenarios ⁢ ∑ i ⁢ ⁢ scenario = 1 N scenarios ⁢ θ i _ ⁡ [ iscenario ] .