Parameter estimation with maximal updated densities
Parameter estimation with maximal updated densities
复制标题
使用最大更新密度的参数估计
DOI：
10.1016/j.cma.2023.115906
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发表时间：
2023
影响因子：
7.2
通讯作者：
Dawson, Clint
中科院分区：
文献类型：
--
作者：
Pilosov, Michael;del-Castillo-Negrete, Carlos;Yen, Tian Yu;Butler, Troy;Dawson, Clint
最近开发的测量理论框架解决了模型的随机逆问题（SIP），其中模型输出数据中的不确定性主要是由于任意性（即，不可约的）模型输入中的不确定性（即，参数）。随后的推理目标是参数的分布。另一种类型的逆问题是在假设随着更多的数据被纳入问题中，这种不确定性应该减少的情况下量化“真实”参数值的估计中的不确定性，即，不确定性被认为是认识性的。这项工作的一个主要贡献是制定和解决这样的参数识别问题（PIP）的测量理论框架内开发的SIP。该方法是新颖的，因为它利用一个随机前向问题（SFP）的解决方案，更新的初始密度仅在参数方向通知的模型输出数据。换句话说，该方法仅在未被数据通知的参数方向上执行“选择性正则化”。该解决方案由最大更新密度（MUD）点定义，其中更新密度定义PIP的测量理论解决方案。这项工作的另一个重要贡献是充分理论的存在性和唯一性的MUD点的线性映射高斯分布。数据构建的感兴趣的数量（QoI）地图也提出和分析，解决PIP在这个测量理论框架内，作为一种手段，减少不确定性的MUD估计。最后，我们证明了该方法的一般适用性的两个问题，涉及空间或时间数据估计不确定的模型参数。第一个问题利用空间数据从一个固定的偏微分方程产生一个不确定的边界条件的MUD估计。第二个问题利用从最先进的先进循环（ADCIRC）模型获得的时间数据，以获得模拟的极端天气事件附近的Shinnecock入口位于美国纽约州长岛外障的不确定风阻力系数的MUD估计。
A recently developed measure-theoretic framework solves a stochastic inverse problem (SIP) for models where uncertainties in model output data are predominantly due to aleatoric (i.e., irreducible) uncertainties in model inputs (i.e., parameters). The subsequent inferential target is a distribution on parameters. Another type of inverse problem is to quantify uncertainties in estimates of “true” parameter values under the assumption that such uncertainties should be reduced as more data are incorporated into the problem, i.e., the uncertainty is considered epistemic. A major contribution of this work is the formulation and solution of such a parameter identification problem (PIP) within the measure-theoretic framework developed for the SIP. The approach is novel in that it utilizes a solution to a stochastic forward problem (SFP) to update an initial density only in the parameter directions informed by the model output data. In other words, this method performs “selective regularization” only in the parameter directions not informed by data. The solution is defined by a maximal updated density (MUD) point where the updated density defines the measure-theoretic solution to the PIP. Another significant contribution of this work is the full theory of existence and uniqueness of MUD points for linear maps with Gaussian distributions. Data-constructed Quantity of Interest (QoI) maps are also presented and analyzed for solving the PIP within this measure-theoretic framework as a means of reducing uncertainties in the MUD estimate. We conclude with a demonstration of the general applicability of the method on two problems involving either spatial or temporal data for estimating uncertain model parameters. The first problem utilizes spatial data from a stationary partial differential equation to produce a MUD estimate of an uncertain boundary condition. The second problem utilizes temporal data obtained from the state-of-the-art ADvanced CIRCulation (ADCIRC) model to obtain a MUD estimate of uncertain wind drag coefficients for a simulated extreme weather event near the Shinnecock Inlet located in the Outer Barrier of Long Island, NY, USA.