Implementation of Accurate Estimation Methodology for Compartmental Models

我的研究兴趣是在实验设计和统计上有意义的，但计算上易处理的房室模型的估计方法的发展。房室模型提供了一个有价值的工具，在分析各种各样的问题，如药物通过身体的动力学或通过示踪实验设计的生态系统的营养物质的流动。在大多数情况下，当设计示踪剂实验时，成本和/或可行性是问题，因为这样的实验通常由于高成本、伦理问题或对生物体的可能损害而不可重复。尽管如此，涉及房室模型的实验的仔细设计可以通过理解系统的生物或生理机制的科学家和具有描述系统的参数或流速的可识别性和稳定性中出现的数学和计算问题的房室分析师之间的适当合作来完成。一旦一个模型，被认为是合理的研究过程中，已经提出，目标是估计模型的参数从一组观察收集的时间。然而，生物数据的非常数方差和/或异常观测值的存在阻碍了普通最小二乘或等权L_2估计的标准应用。虽然L_1模估计可以减少异常值的影响，但由于统计原因，它通常是不可取的。为了获得统计上最优的估计量，工作人员通常使用经验权重执行加权最小二乘，迭代重新加权最小二乘，或者通常使用对数变换来变换数据和/或模型。然而，在实践中，最佳权重是未知的，因此加权或迭代重新加权最小二乘的应用并不简单。此外，涉及当前变换方法的方法，例如Box-Cox变换，虽然成功地稳定了方差，但通常不会产生计算上更需要解决的问题。我的近期研究包括调查的使用和性质的积分变换方法的估计。这种积分变换对于给定的问题应该是“自然的”;自然的是，应用这种变换应该产生一个问题，这个问题在计算上不会比目前的方法更昂贵，但更适合于模型，因为这种变换应该稳定方差，但计算简单。目前，我正在研究这些问题，将拉普拉斯变换应用于线性时不变房室模型。

My research interests are in the design of experiments and the development of statistically meaningful yet computationally tractable estimation methods for compartmental models. Compartmental models provide a valuable tool in analyzing a wide variety of problems, such as the the kinetics of drugs through a body or the flow of nutrients through an ecosystem via the design of tracer experiments. In most cases, cost and/or feasibility are issues when designing a tracer experiment since such experiment is often non-repeatable due to high cost, ethical issues, or possible damage to the organism. Nonetheless, the careful design of an experiment involving compartmental models can be accomplished through proper collaboration between the scientist who has understanding of the biological or physiological mechanism of the system and the compartmental analyst who has knowledge of the mathematical and computational issues that arise in the identifiability and stability of the parameters or flow rates which describe the system. Once a model, deemed reasonable for the process under study, has been proposed, the objective is to estimate the parameters of the model from a set of observations gathered through time. However, the commonly-occurring non-constant variance of biological data and/or the presence of outlying observations discourage standard application of ordinary least squares or equally weighted L_2 estimation. Although L_1-norm estimation would reduce the influence of outliers, for statistical reasons, it is generally not preferred. To obtain statistically optimal estimators, workers often perform weighted least squares using empirical weights, iteratively reweighted least squares, or transform the data and/or the model often using the logarithm transformation. However, in practice, the optimal weights are not known, thus application of weighted or iteratively reweighted least squares is not straightforward. Moreover, methods involving current transformation methodology, such as Box-Cox transformations, while succeeding in stabilizing the variance, often do not yield a computationally more desirable problem to solve. My immediate research consists of investigating the use and properties of integral transform methods in estimation. Such integral transform should be `natural' to a given problem; natural, in that applying such transformation should yield a problem which would be computationally no more costly than current methods but more amenable to the model, in that such transformation should stabilize the variance yet be computationally simple. Currently, I am looking at these issues with the Laplace transform applied to linear time invariant compartmental models.