ENHANCEMENT OF NONLINEAR ESTIMATION CAPABILITY OF MLAB

MLAB非线性估计能力的增强

• 批准号: 3493499
• 负责人: BARRY J BUNOW
• 金额: $ 4.92万
• 依托单位: CIVILIZED SOFTWARE, INC.
• 依托单位国家: 美国
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-09-01 至 1994-02-28
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/3493499
• 关键词: computer data analysis; mathematical model; model design /development; statistics /biometry

The heart of the MLAB modeling language is the facility for parameter estimation in mathematical models by fitting to data. This computation is performed using the Marquardt-Levenburg algorithm and is applicable to nonlinear models subject to linear constraints. By the use of appropriate weighting choices, the algorithm is capable of a variety of extensions, including norms other than L2, iteratively reweighted least squares, and, for special cases only, maximum likelihood estimation. The robustness of the algorithm has been enhanced through the provision of automatically- calculated symbolic partial derivatives, and by heuristic use of gradient search. Despite all these features, there are still many classes of estimation problem that are beyond the current capability of MLAB. These include: more general maximum likelihood estimation, stochastic estimation, and estimation for partial differential equation-defined models. For each of these classes, we have developed new strategies and intend to incorporate them into MLAB. The present proposal deals with three particular aspects of nonlinear estimation that we have identified for enhancement. * generalization of the constraint facility to include nonlinear equality and inequality constraints using Lagrange multiplier techniques. * generalization of the facility for estimation of the confidence intervals and joint confidence regions for parameters in nonlinear models with active constraints. * provision of alternative methods for function optimization that will increase the robustness of parameter estimation for certain classes of nonlinear models. In particular, simplex methods and simulated annealing have been identified as suitable candidates. For Phase I, we will identify a wide range of further extensions to be developed for Phase II.

MLAB建模语言的核心是参数的便利 通过对数据进行拟合来估计数学模型中的值。这项计算是 使用马夸特-莱文伯格算法执行，并适用于 受线性约束的非线性模型。通过使用适当的 加权选择，该算法能够进行各种扩展， 包括L2以外的范数、迭代重新加权的最小二乘，以及， 仅对于特殊情况，最大似然估计。的健壮性 该算法已得到改进，因为提供了自动- 计算符号偏导数，并通过启发式使用梯度 搜索。 尽管有所有这些功能，但仍有许多类别的估计 超出MLAB当前能力范围的问题。这些措施包括： 更一般的最大似然估计、随机估计和 偏微分方程定义模型的估计。对于每一个 这些班级，我们已经制定了新的战略，并打算将 他们进入了MLAB。本提案涉及三个具体方面 我们已经确定了增强的非线性估计。 *将约束机制推广到包括非线性等式 和使用拉格朗日乘子技术的不等式约束。 *推广估计置信度的便利 非线性模型中参数的区间和联合置信域 具有激活的约束。 *为功能优化提供替代方法，以 提高某些类别的参数估计的稳健性 非线性模型。特别是单纯形法和模拟退火法 已被确定为合适的候选人。 对于第一阶段，我们将确定一系列进一步的扩展，包括 为第二阶段开发。