Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data
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DOI：
10.5194/npg-26-227-2019
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发表时间：
2019-04
影响因子：
2.2
通讯作者：
F. Lu;N. Weitzel;A. Monahan
中科院分区：
文献类型：
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作者：
F. Lu;N. Weitzel;A. Monahan
抽象的。虽然非线性随机偏微分方程在时空建模中自然出现，但此类系统的推理通常面临两个主要挑战：稀疏噪声数据和参数估计逆问题的不适定性。为了克服这些挑战，我们通过标准化可能性并通过参数和状态的先验施加物理约束来引入强正则化后验。我们研究了用于古气候重建的物理驱动的非线性随机能量平衡模型（SEBM）中正则化后验的联合参数状态估计。高维后验由粒子吉布斯采样器采样，该采样器将马尔可夫链蒙特卡罗 (MCMC) 方法与利用 SEBM 结构的最佳粒子滤波器相结合。在基于参数的物理范围使用高斯或均匀先验的测试中，正则化后验克服了不适定性并导致物理范围内的样本，从而量化了估计的不确定性。由于病态性和正则化，参数的后验呈现出相对较大的不确定性，因此后验的最大值（即变分方法中的极小值）可能有较大的变化。相比之下，状态的后验通常集中在真实情况附近，基本上滤除观察噪声并减少无约束 SEBM 中的不确定性。
Abstract. While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data and ill-posedness of the inverse problem of parameter estimation. To overcome the challenges, we introduce a strongly regularized posterior by normalizing the likelihood and by imposing physical constraints through priors of the parameters and states. We investigate joint parameter-state estimation by the regularized posterior in a physically motivated nonlinear stochastic energy balance model (SEBM) for paleoclimate reconstruction. The high-dimensional posterior is sampled by a particle Gibbs sampler that combines a Markov chain Monte Carlo (MCMC) method with an optimal particle filter exploiting the structure of the SEBM. In tests using either Gaussian or uniform priors based on the physical range of parameters, the regularized posteriors overcome the ill-posedness and lead to samples within physical ranges, quantifying the uncertainty in estimation. Due to the ill-posedness and the regularization, the posterior of parameters presents a relatively large uncertainty, and consequently, the maximum of the posterior, which is the minimizer in a variational approach, can have a large variation. In contrast, the posterior of states generally concentrates near the truth, substantially filtering out observation noise and reducing uncertainty in the unconstrained SEBM.