2016/03/21 by Ajay Jasra, Kody Law, Jasra, Ajay +4 · 1 citation
Decision Sciences · Engineering · Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #Nuclear reactor physics and engineering #Probabilistic and Robust Engineering Design #Statistical Methods and Inference #stat.CO
paper · pdf · doi:10.48550/arxiv.1603.06381
arxiv created 2016/03/21 · openalex publication_date 2016/03/21 · arxiv updated 2016/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper considers uncertainty quantification for an elliptic nonlocal equation. In particular, it is assumed that the parameters which define the kernel in the nonlocal operator are uncertain and a priori distributed according to a probability measure. It is shown that the induced probability measure on some quantities of interest arising from functionals of the solution to the equation with random inputs is well-defined; as is the posterior distribution on parameters given observations. As the elliptic nonlocal equation cannot be solved approximate posteriors are constructed. The multilevel Monte Carlo (MLMC) and multilevel sequential Monte Carlo (MLSMC) sampling algorithms are used for a priori and a posteriori estimation, respectively, of quantities of interest. These algorithms reduce the amount of work to estimate posterior expectations, for a given level of error, relative to Monte Carlo and i.i.d. sampling from the posterior at a given level of approximation of the solution of the elliptic nonlocal equation.