矩阵的加号逆理论在参数估计中的应用

本文从矩阵的加号逆理论出发,根据求矛盾线性方程组最佳逼近解的方法,建立起一种新的参数估计方法,同时给出了显著性检验方法,这种方法更简单更精确．     

生物种群动态微分方程模型参数估计方法

本文以数值分析和最优化技术的有机结合为基础,提出了一种新的对动态微分方程模型直接进行数据拟合和参数估计方法,并以Logistic微分方程、生物种间竞争关系微分方程以及一种复合形态的Logistic微分方程为例进行了数据拟合试验．结果表明,该方法对各种动态微分方程模型均能进行最优拟合分析并求解其参数．同时发现,以前有的作者〔1,2,3,4,5〕提出的方法所得到的参数估计值存在系统误差且误差较大．     

Thermodynamical model for insertion and aggregate binding of caffeine to the homopolymer poly(riboadenylate) and model choice by data analysis

This paper describes the model used to estimate the parameters of caffeine-poly(riboadenylate) (poly(A)) interactions from corresponding 1H-NMR measurements. The model of insertion and aggregate binding describes the non-cooperative insertion of a molecule C into an interspace between two monomers of a homopolymer in competition with aggregate binding. It contains two binding constants, K1 for insertion and K2 for the interaction of monomeric A units of the polymer with C molecules in bound aggregates, and two cooperativity parameters, Kcc for stacking of C molecules within aggregates and tau which is thought to be due to conformational adaptation of the polymer to those bound aggregates which cover more than one A unit. In contrast to other models, the size of a binding site (within the aggregates) is less than one monomeric unit, with n denoting the maximum number of C molecules per A unit in bound aggregates. The model is developed for general n by means of the method of sequence-generating functions. For n = 2 and n = 3, the correctness of the model treatment was checked by the matrix method. The model is applicable to the binding of aggregates to homopolymers, which are flexible enough to fit their structure to the aggregates.     

A probability model for the number of births in an equilibrium birth process

A probability model for the number of complete conceptions (that is, live births) taking into account foetal wastages, occurring in a couple during a specified period of time (T₀, T₀+T) is developed assuming that the data was collected starting a long time after marriage. A method of estimating some of the underlying parameters is given. The model is applied to data obtained in a Varanasi Survey in 1969–70.     

Finger ridge-count variation among various Subsaharan African groups

This paper addresses the question of the extent to which finger ridge-count data are useful features with which to study population variation in Subsaharan Africa. Each subject was represented by a vector of 20 ridge-counts, a radial and an ulnar count for each digit. Such data were available from 11 African groups, nine of which were indigenous Africans, and two, the South African Colored and South African Indians, contained a portion of non-African ancestory. The ridge-counts were first transformed to principal component scores and these were subjected to multivariate analysis of variance and distance analysis to elucidate intergroup variation. The primary findings were that ridgecounts provide a good reflection of variation on at least two levels, that of African versus non-African, and variation among Africans. Also, the principal components that reveal variation at these two levels are very different. We conclude that ridge-counts can only be useful in population studies if full account is taken of their multicomponent nature.     

MIXED MODEL APPROACHES FOR ESTIMATING GENETIC VARIANCES AND COVARIANCES

The limitations of methods for analysis of variance(ANOVA)in estimating genetic variances are discussed. Among the three methods(maximum likelihood ML, restricted maximum likelihood REML, and minimum norm quadratic unbiased estimation MINQUE)for mixed linear models, MINQUE method is presented with formulae for estimating variance components and covariances components and for predicting genetic effects. Several genetic models, which cannot be appropriately analyzed by ANOVA methods, are introduced in forms of mixed linear models. Genetic models with independent random effects can be analyzed by MINQUE(1)method whieh is a MINQUE method with all prior values setting 1. MINQUE(1)method can give unbiased estimation for variance components and covariance components, and linear unbiased prediction (LUP) for genetic effects. There are more complicate genetic models for plant seeds which involve correlated random effects. MINQUE(0/1)method, which is a MINQUE method with all prior covariances setting 0 and all prior variances setting 1, is suitable for estimating variance and covariance components in these models. Mixed model approaches have advantage over ANOVA methods for the capacity of analyzing unbalanced data and complicated models. Some problems about estimation and hypothesis test by MINQUE method are discussed.     

An ecological example of the application of projection pursuit to compositional data

A modern statistical technique for the exploratory analysis of multivariate data, called projection pursuit, is described. The method consists of the extraction and display of informative one- or two-dimensional projections of the multivariate dataset. Projection pursuit has much scope for application to ecological datasets. The example in this paper concerns element concentrations in soil samples from a coastal embayment on the east coast of Australia. The application attempts to search for patterns in the soils which could be related to vegetation patterns. The compositional nature of the dataset adds a novel element to the methodology.     

Book reviews

The numbers of perch Perca fluviatilis in the Cikola backwater system of the river Danube were estimated by mark-recapture techniques using multiple fishings. Fish were caught by fyke nets and electrical fishing. The latter method was unselective for sex and the catch data could be used to correct the sex bias in the fyke net catches. A population estimate in April of 6059 ind ha^–1 (95% C.L. 5135–7386) for perch > 5 cm was obtained for a 0.6 ha area of backwater and 1665 ind ha^–1 (95% C.L. 1204–2692) in May for a 0.4 ha area of a small bay.     

A METHOD FOR ESTIMATING MASS OF LARGE PINNIPEDS

Fifty-two male elephant seals were weighed and photographed at Año Nuevo State Reserve, California, to establish a predictive relationship between photographically measured morphological variables (length, side area, and girth area) and body mass. Regression of mass on these variables revealed that side area, roughly equivalent to a longitudinal cross-section, was the most useful single variable for predicting mass, and that adding the other two variables to side area slightly improved the accuracy of the photogrammetric technique. Curvilinear regressions based on a power model provided the best predictive relationships. This technique may prove useful for estimating body mass of other pinnipeds.