Before revision:   Our methods first compute parameters that minimize the LDT-rate function over the set of parameters leading to extreme events . These solutions provide asymptotic information about small probability events . We propose a series of methods to refine these estimates, namely methods based on importance sampling and on geometric approximation of the extreme event sets.
After revision:  Our methods first compute parameters that minimize the LDT-rate function over the set of parameters leading to extreme events , using adjoint methods to compute the gradient of this rate function. The minimizers give information about the mechanism of the extreme events as well as estimates of their probability. We then propose a series of methods to refine these estimates, namely methods based on importance sampling and on geometric approximation of the extreme event sets.