逆问题中不确定性量化的标准误差计算：渐近理论与自举法
Standard Error Computations for Uncertainty Quantification in Inverse Problems: Asymptotic Theory vs. Bootstrapping.
作者信息
Banks H T, Holm Kathleen, Robbins Danielle
机构信息
Center for Research in Scientific Computation and Center for Quantitative Sciences in Biomedicine North Carolina State University Raleigh, NC 27695-8212.
出版信息
Math Comput Model. 2010 Nov 1;52(9-10):1610-1625. doi: 10.1016/j.mcm.2010.06.026.
We computationally investigate two approaches for uncertainty quantification in inverse problems for nonlinear parameter dependent dynamical systems. We compare the bootstrapping and asymptotic theory approaches for problems involving data with several noise forms and levels. We consider both constant variance absolute error data and relative error which produces non-constant variance data in our parameter estimation formulations. We compare and contrast parameter estimates, standard errors, confidence intervals, and computational times for both bootstrapping and asymptotic theory methods.
我们通过计算研究了非线性参数依赖动力系统反问题中不确定性量化的两种方法。对于涉及多种噪声形式和水平的数据问题，我们比较了自举法和渐近理论方法。在我们的参数估计公式中，我们既考虑了恒定方差绝对误差数据，也考虑了会产生非恒定方差数据的相对误差。我们比较并对比了自举法和渐近理论方法的参数估计、标准误差、置信区间和计算时间。
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