We have developed a general uncertainty estimation method that allows for the comprehensive search of model posterior space while maintaining a high degree of scalability and computational efficiency. We accomplish this by coupling parameter reduction with an optimally-sparse polynomial interpolation scheme. In contrast to Bayesian inference, which treats the posterior sampling problem as a random process, our method exploits the inherent structure of the posterior model space by estimating it with polynomial interpolation. In either case, the posterior represents the equivalent model space, consistent with our prior knowledge, and is used to estimate the inverse solution uncertainty. We demonstrate the efficiency of our method by comparing results from two EM problems with results for two commonly used Bayesian inference schemes: Gibbs and Metropolis-Hastings.


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