ENHANCEMENT OF NONLINEAR ESTIMATION CAPABILITY OF MLAB

MLAB建模语言的核心是参数化工具， 通过拟合数据进行数学模型中的估计。该计算是 使用Marquardt-Levenburg算法进行，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， 包括除L2之外的范数，迭代重加权最小二乘，以及， 仅在特殊情况下，最大似然估计。的鲁棒性 该算法已通过提供自动- 计算符号偏导数，并通过启发式使用梯度 搜索 尽管有这些特点，仍然有许多类别的估计 这些问题超出了MLAB目前的能力。其中包括： 更一般的极大似然估计，随机估计， 偏微分方程定义模型的估计。中的每 这些课程，我们已经制定了新的战略，并打算纳入 进入MLAB。本建议涉及三个具体方面 非线性估计，我们已经确定的增强。 * 将约束设施推广到包括非线性等式 以及使用拉格朗日乘数技术的不等式约束。 * 置信度估计工具的推广 非线性模型参数的区间和联合置信域 主动约束。 * 提供功能优化的替代方法， 增加某些类别的参数估计的鲁棒性 非线性模型特别是单纯形法和模拟退火 被认为是合适的候选人。 至于第一期，我们会物色多项扩展计划， 为第二阶段开发。

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.