An Estimation Procedure for the Joint Distribution of Spatial Direction and Thickness of Flat Bodies Using Vertical Sections Part I: Theoretical Considerations

In soil micromorphology fissures are considered in vertical sections. To get information about the properties of the soil the joint distribution of spatial direction and width is of interest. The fissures are mathematically generalized to flat bodies which form a stationary weighted surface process with the weight “thickness”. Because of stationarity a joint distribution of spatial direction and thickness exists in a “typical point” of the surface process. A suitable parametric family of distributions is assumed. The corresponding parameters can be estimated from measurements on the vertical sections. But on the sections only the visible thickness and the visible angle of a fissure can be measured. Therefore the joint distribution of these variables is expressed by the joint spatial distribution of spatial direction and thickness. This derived distribution depends on the same parameters. The Chi-Square method is proposed for the parameter estimation. The estimation procedure is demonstrated using the Bingham-Mardia distribution for the direction and the lognormal distribution for the thickness and by defining a way to correlate the mean thickness and the direction.     

A Rapid and Efficient Estimation Procedure for the Negative Binomial Distribution

This paper presents a new noniterative procedure for estimating the parameters of a negative binomial distribution. The procedure uses the first moment equation and an equation based on the weighted sample mean, with weights ω_x∝ α^z. The selection of a value for α is examined. A simulation study has been carried out and also the method has been applied to the 35 data sets analysed by Martin and Katti (1965, Biometrics) in order to compare it with the method of moments and with the method of maximum likelihood (ML). We conclude that the new procedure has greater relative efficiency than the method of moments; it gives estimates which are consistently close to ML and are easy to calculate.     

Mixed Moment Estimation in Hermite Distribution and its Comparison with Other Estimation Procedures from Sample Size Considerations

In this paper (1) expressions (correct to n^?2 terms) for biases, variances, and covariances of the estimators a and b of Hermite distribution with probability generating function Exp[a(t–1) + b(t–1)] are obtained for two mixed moment estimates; (2) for the biases and variance-covariances, approximate regions of the parameter space (a>0, b>0) have been outlined where a sample of size 100 can be considered as “safe” in the sense that contribution of second order terms in them is 5% of that from the first order term; (3) comparison of the biases and variance-covariances of these two sets of estimators are made with those for the moment estimators, maximum likelihood estimates and the even point estimators for a sample of size 100 using the terms up to order n^?2; (4) the comparisons based on n^?2 terms in (3) have not only provided information on the estimation procedures included in the Hermite distribution, but also demonstrated the importance of higher order terms in the sampling properties of the various alternative techniques for the Hermite distribution.     

Adsorption of Antimony on Sediments from Typical Water Systems in China: A Comparison of Sb(III) and Sb(V) Pattern

The present work investigated the adsorption of Sb(III) and Sb(V) on five sediment samples (Pearl River, Yangtze River, Yellow River, Yongding River, and Liao River) from typical water systems in China and the adsorption of Sb(V) on Pearl River sediment with different organic carbon (OC) fractions using batch experiments. In order to assess the contributions of sedimentary organic components to the overall adsorption of pentavalent Sb on sediments, one sediment sample was treated by commonly used chemical and physical methods to remove different organic components. Experimental data of Sb(III) and Sb(V) adsorption on five sediments were successfully modeled using the Freundlich (r² > 0.96) isotherm. In general, the sediments with high Fe and Al oxide contents and total organic carbon (TOC) had higher Sb(III) and Sb(V) adsorption than the sediments containing small amounts of Fe and Al oxides and TOC. Dissolved organic carbon (DOC) in sediment promoted the adsorption of Sb(V), and humin fractions and black carbon-like material in sediment had a high affinity for Sb(V).     

New class of Johnson distributions and its associated regression model for rates and proportions

By starting from the Johnson distribution pioneered by Johnson ( 1949 ), we propose a broad class of distributions with bounded support on the basis of the symmetric family of distributions. The new class of distributions provides a rich source of alternative distributions for analyzing univariate bounded data. A comprehensive account of the mathematical properties of the new family is provided. We briefly discuss estimation of the model parameters of the new class of distributions based on two estimation methods. Additionally, a new regression model is introduced by considering the distribution proposed in this article, which is useful for situations where the response is restricted to the standard unit interval and the regression structure involves regressors and unknown parameters. The regression model allows to model both location and dispersion effects. We define two residuals for the proposed regression model to assess departures from model assumptions as well as to detect outlying observations, and discuss some influence methods such as the local influence and generalized leverage. Finally, an application to real data is presented to show the usefulness of the new regression model.     

Logistic方程参数估计中的错误与修正

Logistic方程在种群生态学研究中被广泛应用,其积分式为N=k／（1＋e~（a-rt））,式中e~a=（k-N_0）／N_0。以往对该模型参数的各种估计方法,均将r,K和a作为三个相互独立的参数对待,而与e~a=（K-N_0）/N_0的假设相矛盾。由此估计出的参数K和a使实验初值N_0（t=0时的N值）发生偏离。笔者认为N_0是一个不带随机误差的常数,a值决定于K和N_0,而不是一个独立的参数,因而以往的参数估计方法是错误的,必须予以修正。本文提出了具体的修正方法,即用Marquardt方法或单纯形加速法求参数r和K,然后根据实验初值N_0求a,从而使Logistic微积分方程的共同参数r和K的估计一致。     

Maximum Likelihood Methods for Fitting the Burr Type XII Distribution to Life Test Data

This paper describes mathematical and computational methodology for estimating the parameters of the Burr Type XII distribution by the method of maximum likelihood. Expressions for the asymptotic variances and covariances of the parameter estimates are given, and the modality of the log-likelihood and conditional log-likelihood functions is analyzed. As a result of this analysis for various a priori known and unknown parameter combinations, conditions are given which guarantee that the parameter estimates obtained will, indeed, be maximum likelihood estimates. An efficient numerical method for maximizing the conditional log-likelihood function is described, and mathematical expressions are given for the various numerical approximations needed to evaluate the expressions given for the asymptotic variances and covariances of the parameter estimates. The methodology discussed is applied in a numerical example to life test data arising in a clinical setting.     

Markov Random Field Modeling of the Spatial Distribution of Proteins on Cell Membranes

Cell membranes display a range of receptors that bind ligands and activate signaling pathways. Signaling is characterized by dramatic changes in membrane molecular topography, including the co-clustering of receptors with signaling molecules and the segregation of other signaling molecules away from receptors. Electron microscopy of immunogold-labeled membranes is a critical technique to generate topographical information at the 5–10 nm resolution needed to understand how signaling complexes assemble and function. However, due to experimental limitations, only two molecular species can usually be labeled at a time. A formidable challenge is to integrate experimental data across multiple experiments where there are from 10 to 100 different proteins and lipids of interest and only the positions of two species can be observed simultaneously. As a solution, we propose the use of Markov random field (MRF) modeling to reconstruct the distribution of multiple cell membrane constituents from pair-wise data sets. MRFs are a powerful mathematical formalism for modeling correlations between states associated with neighboring sites in spatial lattices. The presence or absence of a protein of a specific type at a point on the cell membrane is a state. Since only two protein types can be observed, i.e., those bound to particles, and the rest cannot be observed, the problem is one of deducing the conditional distribution of a MRF with unobservable (hidden) states. Here, we develop a multiscale MRF model and use mathematical programming techniques to infer the conditional distribution of a MRF for proteins of three types from observations showing the spatial relationships between only two types. Application to synthesized data shows that the spatial distributions of three proteins can be reliably estimated. Application to experimental data provides the first maps of the spatial relationship between groups of three different signaling molecules. The work is an important step toward a more complete understanding of membrane spatial organization and dynamics during signaling.     

BAYESian Point Estimation of the Unknown Upper Limit of a Uniform Distribution

BAYESian fixed sample size and sequential procedures are considered for the estimation of the unknown parameter v of a uniform distribution over (0, v), under several loss functions.     

Bayesian Reliability Estimation of a Two-parameter Cauchy Distribution

This paper gives an approximate Bayes procedure for the estimation of the reliability function of a two-parameter Cauchy distribution using Jeffreys' non-informative prior with a squared-error loss function, and with a log-odds ratio squared-error loss function. Based on a Monte Carlo simulation study, two such Bayes estimators of the reliability are compared with the maximum likelihood estimator.     

Estimation of additive genetic variance in commercial layer poultry and simulated populations under selection

Changes in genetic parameters over generations for a selected commercial population and simulated populations of poultry with different sizes were studied. The traits analyzed from the commercial population were rate of lay, age at first egg, egg weight, deformation, and body weight. In the simulated population, a trait measured on both sexes and a sex-limited trait, measured only on one sex, each with a heritability of 0.1 and 0.5, were analyzed. In the commercial and simulated populations, males and females were selected on the basis of family selection indexes and data was available only after many generations of selection. Parameters for each generation were estimated by fitting an animal model using derivative free maximum likelihood (DFREML) with different data structures. In structure 1, data included the given (base) generation for which the parameters were to be estimated, and all subsequent generations. In structure 2, only data on birds in the given generation and their progeny were included. In both structures, parents of base-generation birds were assumed unrelated and pedigrees traced back to these parents. With commercial data using structure 1, estimates of _a ² and h² decreased by 14 to 37% across five generations. With structure 2, no trends were observed, though estimates were lower than for structure 1. For simulated data, with a heritability of 0.1, both structures yielded apparently unbiased estimates of the observed additive genetic variances in the (selected) base generation, no matter how many generations of data were utilized, for both sex-limited and normal traits. However, with a heritability of 0.5 the estimated additive genetic variance for both types of trait decreased with a decrease in the number of generations used in the estimation. Estimates based on the first two generations underestimated, while estimates based on five generations of data overestimated, the observed genetic variances in the defined base. The combinations of conditions that lead to varying degrees of bias remain undefined.     

Comparison of Two New Robust Parameter Estimation Methods for the Power Function Distribution

Estimation of any probability distribution parameters is vital because imprecise and biased estimates can be misleading. In this study, we investigate a flexible power function distribution and introduced new two methods such as, probability weighted moments, and generalized probability weighted methods for its parameters. We compare their results with L-moments, trimmed L-moments by a simulation study and a real data example based on performance measures such as, mean square error and total deviation. We concluded that all the methods perform well in the case of large sample size (n>30), however, the generalized probability weighted moment method performs better for small sample size.     

Estimation of Linkage and Association from Allele Transmission Data

The TDT provides a hypothesis test for the presence of linkage or association (linkage disequilibrium). However, since the TDT is a single test statistic, it cannot be used to separate association and linkage. The importance of this difficulty, following a significant TDT result, has been recently emphasized by Whittaker , Denham and Morris (2000), who alert the community to the possibility that a significant TDT may result from loose linkage and strong association, or from tight linkage and weak association. To attack this problem we start with the parametric model for family‐based allele transmission data of Sham and Curtis (1995) (or Sham (1998)) and find that the parameters in the model are not always identifiable. So we introduce a reparameterization that resolves the identifiability issues and leads to a valid likelihood ratio (LR) test for linkage. Since the linkage and association parameters are both of interest, we next introduce and apply an integrated likelihood (IL) approach to provide separate point estimates and confidence intervals for these parameters. The estimates are shown to have generally small bias and mean square error, while the confidence intervals have good average length and coverage probabilities. We compare the power of the IL approach for testing linkage and, separately association, with the TDT and LR.     

The Planning of Sample Sizes for Maximum Likelihood Estimation of the Parameters of the Weibull Distribution

Based on maximum likelihood estimators the problem of setting confidence limits for the scale and shape parameters of the Weibull distribution with two parameters is considered. Approximation formulae for the determination of sample sizes for the parameter estimation are given for complete and type II censored samples.     

Estimation and Prediction With HIV-Treatment Interruption Data

We consider longitudinal clinical data for HIV patients undergoing treatment interruptions. We use a nonlinear dynamical mathematical model in attempts to fit individual patient data. A statistically-based censored data method is combined with inverse problem techniques to estimate dynamic parameters. The predictive capabilities of this approach are demonstrated by comparing simulations based on estimation of parameters using only half of the longitudinal observations to the full longitudinal data sets.     

利用次序统计量估计种群的平均寿命

本文讨论威布尔分布Ｗ（α,λ）中次序统计量的分布;建立了用次序统计量对威布尔分布进行参数估计,进而估计种群平均寿命和方差的方法,该方法可广泛用于可靠性统计产品平均寿命和方差的估计。     

Naturalism, evidence and creationism: The case of Phillip Johnson

Phillip Johnson claims that Creationism is a better explanation of the existence and characteristics of biological species than is evolutionary theory. He argues that the only reason biologists do not recognize that Creationist's negative arguments against Darwinism have proven this is that they are wedded to a biased ideological philosophy —Naturalism — which dogmatically denies the possibility of an intervening creative god. However, Johnson fails to distinguish Ontological Naturalism from Methodological Naturalism. Science makes use of the latter and I show how it is not dogmatic but follows from sound requirements for empirical evidential testing. Furthermore, Johnson has no serious alternative type of positive evidence to offer for Creationism, and purely negative argumentation, despite his attempt to legitimate it, will not suffice.     

Estimation of the proliferation and maturation functions in a physiologically structured model of thymocyte development

The thymus provides a stable microenvironment for post-natal thymocyte development that is finely regulated by a complicated network of cytokines, chemokines, cell-cell contacts, etc., the dysregulations of which contribute to many immunologic diseases including malignant lymphomas. A physiologically structured model in the form of first order partial differential equation (PDE) was developed to simulate the whole process. The combined effects of the thymic microenvironment were conceptualized into two (proliferation and differentiation) fields to serve as kernels of the PDE. In this paper, a novel method is developed to estimate the maturity-time structures of the two fields based solely on cell population data that are experimentally viable. Numerical examples demonstrate the effectiveness of the present method in revealing the two-dimensional (maturity and time) landscapes of the thymic microenvironment.      

Probabilistic Estimation of Regional Dietary Exposure to Dioxins in Fish in Japan on the Basis of Market and Fish Distribution Network Data

Dietary consumption of fish is the greatest contributor to dioxin exposure of the general population in Japan. Unlike with other routes of exposure to dioxins, exposure via foodstuffs does not necessarily occur from local sources. Clarifying the distribution of fish from the catch area to local markets helps to control dioxin exposure from the head of the distribution chain down. We analyzed the data from 30 major central wholesale fish markets to determine both the market share of fish by catch area and the market share of major fish types in fish consumption markets. Probabilistic estimation of dietary exposure of the general population to dioxins in fish was conducted in seven regions in Japan. Probabilistic density functions (PDFs) were assigned to express the variability of data from monitoring of dioxin levels in fish by catch area or by fish type. From histograms of dioxin levels in fish by catch area, the mean and 5th to 95th percentile range of dietary exposure to dioxins in the region with the largest 95th percentile value were estimated, respectively, as 55.5 and 12.9–172.9 pg-TEQ/day. No statistically significant differences in dietary exposure to dioxins in fish were observed among the seven regions. Some specific coastal catch areas and some types of fish that had a greater impact than others on exposure were pinpointed for each region.