Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems

作者：Lu Fei; Morzfeld Matthias^*; Tu Xuemin; Chorin Alexandre J

来源：Journal of Computational Physics, 2015, 282: 138-147.

DOI：10.1016/j.jcp.2014.11.010

• Polynomial chaos expansion
• Bayesian inverse problem
• Monte Carlo sampling

Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpensively. We show, by analysis and example, that when the data contain significant information beyond what is assumed in the prior, the surrogate posterior can be very different from the posterior, and the resulting estimates become inaccurate. One can improve the accuracy by adaptively increasing the order of the polynomial chaos, but the cost may increase too fast for this to be cost effective compared to Monte Carlo sampling without a surrogate posterior.

• 出版日期2015-2-1