用改进的高斯—牛顿最小二乘法估测非线性生长曲线的参数

本文讨论了用改进的高斯－牛顿最小二乘法估测非线性参数的方法,并用肉鸡生长曲线拟合实例给以示范。     

度量误差对模型参数估计值的影响及参数估计方法的比较研究

基于模型V=aDb,首先在Matlab下用模拟实验的方法,研究了度量误差对模型参数估计的影响,结果表明:当V的误差固定而D的误差不断增大时,用通常最小二乘法对模型进行参数估计,参数a的估计值不断增大,参数b的估计值不断减小,参数估计值随着 D的度量误差的增大越来越远离参数真实值;然后对消除度量误差影响的参数估计方法进行研究,分别用回归校准法、模拟外推法和度量误差模型方法对V和D都有度量误差的数据进行参数估计,结果表明:回归校准法、模拟外推法和度量误差模型方法都能得到参数的无偏估计,克服了用通常最小二乘法进行估计造成的参数估计的系统偏差,结果进一步表明度量误差模型方法优于回归校准法和模拟外推法．     

Non-Iterative Least Squares Estimation of Missing Values in Hyper-Graeco-Latin Square Designs

In this paper an attempt has been made to obtain explicit expressions for the estimators of the several missing values in hyper-graeco-latin square designs. Further it has been shown that the estimates of the missing values in latin square designs and graeco-latin square designs are obtained as a particular case of the estimates of the missing values in hyper-graeco-latin square designs.     

Non-Iterative Least Squares Estimation of Missing Values in Graeco-Latin Square Designs

The present paper deals with the estimation of several missing values in Graeco-Latin Square-designs. When the observations are missing in a particular pattern, explicit computable expressions are presented for the estimators of the missing values. This procedure is illustrated with the help of a numerical example.     

Parameter Estimation for the Compartmental Model

An estimation procedure is obtained for a stochastic compartmental model. Compartmental analysis assumes that a system may be divided into homogeneous components, or compartments. The main theory for the compartmental system was studied by Matis and Hartley (1971) with a discrete population in a steady state. All the transitions among the particles are considered to be stochastic in nature. An estimation procedure, Regular Best Asymptotic Normal (RBAN), discussed by Chiang (1956) is investigated for a stochastic m-compartmental system. The detailed proof of the procedure is provided here. Asymptotic properties for the estimator has been studied and computation has been carried out on our proposed nonlinear model. The downhill simplex search method, originally developed by Nelder and Mead (1965), and applied to minimize our quadratic form is inherently nonlinear in nature, thus avoiding the need to evaluate any derivative for point estimation of the parameters. The procedure applied to an experimental situation involving two compartments gives very encouraging results.     

Non-Iterative Least Squares Estimation of Missing Values in Replicated Latin Square Designs

In this paper an attempt has been made to estimate several missing values in replicated latin square designs. The explicit computable expressions for the non-iterative least squares estimates of the missing values are presented for particular patterns of missing values.     

基于偏最小二乘回归的中国青春期男性肺活量参考值与地理因素的关系

目的：为制定中国青春期男性肺活量参考值的统一标准提供科学依据.方法：搜集了中国用肺量计法测定72个单位的213881例健康青春期男性肺活量参考值.运用相关分析的方法研究了其与海拔高度（X_1）,年日照时数（X_2）,年平均相对湿度（X_3）,年平均气温（X_4）,年降水量（X_5）,气温年较差（X_6）,年平均风速（X_7）的关系.结果：发现青春期男性肺活量参考值与地理因素之间有显著的相关关系.用偏最小二乘回归分析的方法建立了青春期男性肺活量参考值与地理因素的回归模型：Y=3024.77-0.131640X_1＋0.022388X_2＋2.381548X_3-1.344117X_4-0.030850X_5＋7.881706X_6＋39.820870X_7±557.93,并用Arcgis软件中的空间差值内插出中国青春期男性肺活量参考值的空间趋势分布图.结论：知道中国某地的地理因素,就可用此模型估算该地区青春期男性肺活量参考值,同时也可用空间趋势图直观的得到中国任何地方的青春期男性肺活量参考值.     

推广的生长曲线模型的协方差不变最小二乘无偏估计(Ⅰ)

本文用投影理论及矩阵的谱分解方法,找出了推广的生长曲线模型的未知协方差矩阵∑及tr(C∑)在一定条件下的不变量小二乘无偏估计,为以后更深入的研究奠定基础。     

用度量误差模型方法编制相容的生长过程表和材积表

指出了按照常规方法建立的生长模型和材积模型不相容的原因、利用两阶段度量误差模型方法估计生长模型和材积模型的参数,进而编制相容的生长过程表和材积表．     

Parameter Estimation and Model Selection in Computational Biology

A central challenge in computational modeling of biological systems is the determination of the model parameters. Typically, only a fraction of the parameters (such as kinetic rate constants) are experimentally measured, while the rest are often fitted. The fitting process is usually based on experimental time course measurements of observables, which are used to assign parameter values that minimize some measure of the error between these measurements and the corresponding model prediction. The measurements, which can come from immunoblotting assays, fluorescent markers, etc., tend to be very noisy and taken at a limited number of time points. In this work we present a new approach to the problem of parameter selection of biological models. We show how one can use a dynamic recursive estimator, known as extended Kalman filter, to arrive at estimates of the model parameters. The proposed method follows. First, we use a variation of the Kalman filter that is particularly well suited to biological applications to obtain a first guess for the unknown parameters. Secondly, we employ an a posteriori identifiability test to check the reliability of the estimates. Finally, we solve an optimization problem to refine the first guess in case it should not be accurate enough. The final estimates are guaranteed to be statistically consistent with the measurements. Furthermore, we show how the same tools can be used to discriminate among alternate models of the same biological process. We demonstrate these ideas by applying our methods to two examples, namely a model of the heat shock response in E. coli, and a model of a synthetic gene regulation system. The methods presented are quite general and may be applied to a wide class of biological systems where noisy measurements are used for parameter estimation or model selection.