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．     

度量误差模型及其应用

本文介绍度量误差模型的基本概念和参数估计的基本结果以及与通常回归之间的关系．并讨论了这个模型在生物学中应用的可能性．     

含度量误差的黑龙江省主要树种生物量相容性模型

基于516株样木的生物量数据,采用非线性度量误差模型理论和方法,构建了黑龙江省15个主要树种(组)总生物量与地上、地下、树干、树冠、树枝、树叶6个分项生物量以及分项生物量间的相容性生物量模型,分别选出各树种总生物量和各分项生物量的最优模型,采用比值函数分级联合控制方程组构建了以总生物量为基础的相容性模型,并采用对数变换对总生物量模型消除异方差,采用加权回归对各分项生物量模型消除异方差.结果表明:本文所建的15个树种(组)相容性生物量模型中,总生物量的预估精度最高,达到90％以上;其次是地上部分生物量和树干生物量,预估精度在87.5％以上;地下部分、树冠、树枝和树叶生物量的预估精度相对较低,但绝大多数树种(组)的预估精度在80％以上;所有树种(组)总生物量、地上部分生物量、树干生物量模型的模拟效率(EF)值达0.9以上,绝大多数树种(组)的地下部分、树冠、树枝、树叶生物量模型的EF值在0.8以上.     

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．     

非线性模型参数估计的一种新方法

本文以正交试验为工具,利用序贯思想,提出了非线性模型参数估计的正交试验法。该法简单易行,便于推广,且与Gauss-Newton法的结果相当。     

线性度量误差模型的参数估计法与最小二乘法的关系

线性度量误差模型的参数分为度量误差向量的参数和非度量误差向量的参数,本文的研究表明,不论是非度量误差向量的参数估计还是度量误差向量的参数估计都可以由最小二乘估计法推广得到.     

一种自适应的种群增长模型及参数估计

通过对种群增长的非线性制约机制的数学形态分析,提出了一种新的种群增长数学模型ｄｘ／ｄｔ＝ｒｘ（１－（ｘ／ｘｍ）＾ｓ）其解析解为：ｘ（ｔ）＝ｘｍ／（１＋（ｘ＾ｓｍ／ｘ＾ｓ０－１）ｅ＾－ｒｓｔ）＾１／ｓ该模型当非线性密度制约指数ｓ〈１,ｓ＝１,ｓ〉１及ｓ→∞时分别对尖于ＳｍｉｔｈＬｏｇｉｓｔｉｃ,崔－Ｌａｗｓｏｎ及指数增长模型,具有自适应性,本文还提出了一种种群增长模型对数估计的搜索寻优方法,只要给出     

多元统计中Logistic回归模型参数估计的一种方法及应用

本文提出一多元统计中Logistics回归模型参数的估计方法──极大似然估计法,使得很容易在计算机上应用,并建立了大兴安岭地区秋季人为火发生预报模型。     

东北林区4个天然针叶树种单木生物量模型误差结构及可加性模型

基于276株实测生物量数据,构建了东北林区红松、臭冷杉、红皮云杉和兴安落叶松4个天然针叶树种总量及各分项生物量一元、二元可加性生物量模型.采用似然分析法判断总量及各分项生物量异速生长模型的误差结构(可加型或相乘型),而模型参数估计采用非线性似乎不相关回归模型方法.结果表明: 经似然分析法判断,4个天然树种总量及各分项生物量异速生长模型的误差结构都是相乘型的,对数转换的可加性生物量可以被选用.各树种可加性生物量模型的调整后确定系数R_a²为0.85～0.99,平均相对误差为-7.7%～5.5%,平均相对误差绝对值<30.5%.增加树高可以显著提高各树种可加性生物量模型的拟合效果和预测能力,而且总量、地上和树干生物量模型效果较好,树根、树枝、树叶和树冠生物量模型效果较差.所建立的可加性生物量模型的预测精度为77.0%～99.7%(平均92.3%),可以很好地预估东北林区天然红松、臭冷杉、红皮云杉和兴安落叶松的生物量.
     

站点CERES-Rice模型区域应用效果和误差来源

作物区域模拟是利用有限的空间数据,最大限度地反映出生育期、产量等作物性状的时空变化规律.由于目前的作物模型大多是田间尺度的站点模型,把它运用到区域水平的效果如何研究甚少.文章利用CERES-Rice模型,对作物模型在我国的区域应用效果进行了分析.首先利用田间观测数据在各实验点上对模型进行了详细的站点校准,以验证模型在我国的模拟能力;然后以我国水稻生态区(精确到亚区)为单位,运用均方根差(RMSE)法进行了区域校准和验证;最后利用区域校准后的CERES-Rice模型,模拟了1980～2000年的网格(50km×50km)水稻产量,并与同期农调队调查产量进行统计比较,以验证区域应用的效果,为区域模拟的推广和应用提供参考.结果表明:经过空间校准后的CERES-Rice模型,在水稻的主产区1～4区(占种植面积的95%)模拟的平均产量与调查产量相对均方根差在22%以内,两者的符合度也较好,个别区域(5、6) RMSE%在24%～30%之间;1980～2000年水稻各产区模拟的平均产量与调查产量随时间变化趋势也具有一定的一致性;全国1896个网格中,大部分网格(71.01%)模拟的21年水稻年产量与调查产量的RMSE%在30%之内,且大部分分布在水稻主产区,考虑到水稻种植面积的权重后,认为利用区域校准和验证后的CERES-Rice模型进行水稻区域模拟,可以反映出产量的时空分布特征,能够为宏观决策提供相应的信息.但目前区域模拟中还存在着一定的误差,有待今后进一步研究.     

AN EIGENVECTOR METHOD FOR ESTIMATING PHYLOGENETIC INERTIA

We propose a new method to estimate and correct for phylogenetic inertia in comparative data analysis. The method, called phylogenetic eigenvector regression (PVR) starts by performing a principal coordinate analysis on a pairwise phylogenetic distance matrix between species. Traits under analysis are regressed on eigenvectors retained by a broken-stick model in such a way that estimated values express phylogenetic trends in data and residuals express independent evolution of each species. This partitioning is similar to that realized by the spatial autoregressive method, but the method proposed here overcomes the problem of low statistical performance that occurs with autoregressive method when phylogenetic correlation is low or when sample size is too small to detect it. Also, PVR is easier to perform with large samples because it is based on well-known techniques of multivariate and regression analyses. We evaluated the performance of PVR and compared it with the autoregressive method using real datasets and simulations. A detailed worked example using body size evolution of Carnivora mammals indicated that phylogenetic inertia in this trait is elevated and similarly estimated by both methods. In this example, Type I error at α = 0.05 of PVR was equal to 0.048, but an increase in the number of eigenvectors used in the regression increases the error. Also, similarity between PVR and the autoregressive method, defined by correlation between their residuals, decreased by overestimating the number of eigenvalues necessary to express the phylogenetic distance matrix. To evaluate the influence of cladogram topology on the distribution of eigenvalues extracted from the double-centered phylogenetic distance matrix, we analyzed 100 randomly generated cladograms (up to 100 species). Multiple linear regression of log transformed variables indicated that the number of eigenvalues extracted by the broken-stick model can be fully explained by cladogram topology. Therefore, the broken-stick model is an adequate criterion for determining the correct number of eigenvectors to be used by PVR. We also simulated distinct levels of phylogenetic inertia by producing a trend across 10, 25, and 50 species arranged in “comblike” cladograms and then adding random vectors with increased residual variances around this trend. In doing so, we provide an evaluation of the performance of both methods with data generated under different evolutionary models than tested previously. The results showed that both PVR and autoregressive method are efficient in detecting inertia in data when sample size is relatively high (more than 25 species) and when phylogenetic inertia is high. However, PVR is more efficient at smaller sample sizes and when level of phylogenetic inertia is low. These conclusions were also supported by the analysis of 10 real datasets regarding body size evolution in different animal clades. We concluded that PVR can be a useful alternative to an autoregressive method in comparative data analysis.     

TWO MODELS FOR ESTIMATING THE DISCRIMINABILITY OF FOODS AND BEVERAGES

In order to evaluate the suitability of signal detection theory methods for assessing the discriminability of foods and beverages, the discriminability of two dairy milk products that differed in fat content was measured with two detection-theoretic methods: the single-interval rating method, and the same-different method. The nominal fat contents of the milk products were 0.1 and 1.6%. Measures of discriminability for three observers were derived by fitting receiver operating characteristics (ROCs) based on equal-variance normal models to the ratings of each observer with a procedure that combined jackknifing and maximum-likelihood estimation. The fitted ROCs provided a good fit to the data indicating that the equal-variance models were appropriate for these tasks. The best-fitting estimates of d' obtained for each task were not significantly different, demonstrating that d' is a measure of sensitivity that is largely independent of the task from which it is determined. However, estimates of proportion correct obtained for each task were shown to be significantly different.     

ESTIMATING UNCERTAINTY IN MULTIVARIATE RESPONSES TO SELECTION

Predicting the responses to natural selection is one of the key goals of evolutionary biology. Two of the challenges in fulfilling this goal have been the realization that many estimates of natural selection might be highly biased by environmentally induced covariances between traits and fitness, and that many estimated responses to selection do not incorporate or report uncertainty in the estimates. Here we describe the application of a framework that blends the merits of the Robertson–Price Identity approach and the multivariate breeder's equation to address these challenges. The approach allows genetic covariance matrices, selection differentials, selection gradients, and responses to selection to be estimated without environmentally induced bias, direct and indirect selection and responses to selection to be distinguished, and if implemented in a Bayesian‐MCMC framework, statistically robust estimates of uncertainty on all of these parameters to be made. We illustrate our approach with a worked example of previously published data. More generally, we suggest that applying both the Robertson–Price Identity and the multivariate breeder's equation will facilitate hypothesis testing about natural selection, genetic constraints, and evolutionary responses.     

A METHOD FOR ASSESSING PHYLOGENETIC LEAST SQUARES MODELS FOR SHAPE AND OTHER HIGH‐DIMENSIONAL MULTIVARIATE DATA

Studies of evolutionary correlations commonly use phylogenetic regression (i.e., independent contrasts and phylogenetic generalized least squares) to assess trait covariation in a phylogenetic context. However, while this approach is appropriate for evaluating trends in one or a few traits, it is incapable of assessing patterns in highly multivariate data, as the large number of variables relative to sample size prohibits parametric test statistics from being computed. This poses serious limitations for comparative biologists, who must either simplify how they quantify phenotypic traits, or alter the biological hypotheses they wish to examine. In this article, I propose a new statistical procedure for performing ANOVA and regression models in a phylogenetic context that can accommodate high‐dimensional datasets. The approach is derived from the statistical equivalency between parametric methods using covariance matrices and methods based on distance matrices. Using simulations under Brownian motion, I show that the method displays appropriate Type I error rates and statistical power, whereas standard parametric procedures have decreasing power as data dimensionality increases. As such, the new procedure provides a useful means of assessing trait covariation across a set of taxa related by a phylogeny, enabling macroevolutionary biologists to test hypotheses of adaptation, and phenotypic change in high‐dimensional datasets.     

ALGORITHM FOR APPLICATION OF FOURIER ANALYSIS FOR BIORHYTHMIC BASELINES OF PHARMACODYNAMIC INDIRECT RESPONSE MODELS

The change of an indirect pharmacological response R(t) can be described by a periodic time-dependent production rate k_in (t) and a first-order loss constant k_out. If k_in(t) follows some biological rhythm (e.g., circadian), then the response R(t) also displays a periodic behavior. A new approach for describing the input function in indirect response models with biorhythmic baselines of physiologic substances is introduced. The present approach uses the baseline (placebo) response R_b(t) to recover the equation for k_in(t). Fourier analysis provides an approximate equation for R_b(t) that consists of terms (usually two or three) of the Fourier series (harmonics) that contribute most to the overall sum. The model differential equation is solved backward for k_in(t), yielding the equation involving R_b(t). A computer program was developed to perform the square L²-norm approximation technique. Fourier analysis was also performed based on nonlinear regression. Cortisol suppression after inhalation of fluticasone propionate (FP) was modeled based on the inhibition of the secretion rate k_in(t) using ADAPT II. The pharmacodynamic parameters k_out and IC₅₀ were estimated from the model equation with k_in(t) derived by the new approach. The proposed method of describing the input function needs no assumption about the behavior of k_in(t), is as efficient as methods used previously, and is more flexible in describing the baseline data than the nonlinear regression method. (Chronobiology International, 17(1), 77–93, 2000)     

心肌振荡模型的非线性动力学研究

通过计算机对心肌振荡模型的研究,得到它在单刺激下的相角转移曲线.用相角转移曲线研究了振子在不同周期刺激下表现出来的锁相、分叉及混沌现象,进而对某些常见的心律失常产生的机制进行了讨论.     

单纯形加速法拟合生态学中的非线性模型

本文以Logistic模型,Taylor幂法则模型,Holling功能反应模型,以及种群内禀增长力Rm等模型的拟合和参数估计为例,探讨单纯形加速法在生态模型优化拟合和参数估计中的应用.结果表明,单纯形加速法拟合生态学中的非线性模型不仅适用广泛,而且拟合过程是直接求原来非线性模型的最优拟合,因而优于生态学中通常使用的将原模型“线性化后再拟合”的方法,而与其它一些最优化方法,如:麦夸方法、枚举选优法等比较,由于单纯形法不需计算目标函数的偏导数,因而计算不受目标函数及其偏导函数复杂程度的限制,而且对于各种模型其求优计算过程十分相似,可以编制统一的计算程序.本研究所编制的计算机程序对于本文未提到的其它一些模型也是完全适用的,在应用时仅需修改定义目标函数的自定义函数语句即可.研究也发现,在求优过程中,只要搜索系数选择适当和实际数据合理,是可以保证寻优成功的.     

一种以准DOG分布为基元的体视匹配算法

本文提出了一种新体视的匹配算法,其特点是:(1)以准DOG分布为基元;(2)以同源性、唯一性、顺序性为约束;(3)本质上是一种协同算法。理论分析和实际计算表明,该算法是合理的,有效的。最近的一些心理物理学结果是支持我们的这个算法的。