Characterization of the Negative Binomial and Gamma Distributions

Characterization of the negative binomial and gamma distributions by a conditional distribution and a linear regression, and the gamma distribution by the negative binomial distribution are given. An application to a random shock model is discussed.     

Towards objectivity in vegetation classification: the example of the Austrian forests

We present a numerical classification of 2145 objectively sampled relevés from the entire forest area of Austria (Central Europe). The sample sites were selected by a combined method involving a systematic matrix and stratified random sampling. A TWINSPAN classification led to 32 clusters which are described in detail. Three main groups can be distinguished: (1) Alpine-dinaric coniferous forests on carbonate soils, (2) Coniferous forests on acid soils and (3) Deciduous forests. These groups correspond with accuracy to the classes Erico-Pinetea, Vaccinio-Piceetea and Querco-Fagetea in the traditional Braun-Blanquet system. Thus, the value of the Braun-Blanquet approach is supported by more or less objective sampling and numerical classification methods. The assumption of the objective existence of ecological species groups is strongly supported, too. Moreover, our results may help to solve some controverse points discussed in the European forest classification regarding the delimination between the three mentioned classes. This revised version was published online in August 2006 with corrections to the Cover Date.     

选择回归方程自变量的条件数法及其在RK手术中的应用

选择合适的自变量是确定线性回归模型的首要问题,本文以消除自变量之间的复共线性为目标,介绍了一种选择回归方程自变量的条件数法,并在ＲＫ手术的结果预测问题中采用了这一方法。     

Generalized varying coefficient models for longitudinal data

We propose a generalization of the varying coefficient modelfor longitudinal data to cases where not only current but alsorecent past values of the predictor process affect current response.More precisely, the targeted regression coefficient functionsof the proposed model have sliding window supports around currenttime t. A variant of a recently proposed two-step estimationmethod for varying coefficient models is proposed for estimationin the context of these generalized varying coefficient models,and is found to lead to improvements, especially for the caseof additive measurement errors in both response and predictors.The proposed methodology for estimation and inference is alsoapplicable for the case of additive measurement error in thecommon versions of varying coefficient models that relate onlycurrent observations of predictor and response processes toeach other. Asymptotic distributions of the proposed estimatorsare derived, and the model is applied to the problem of predictingprotein concentrations in a longitudinal study. Simulation studiesdemonstrate the efficacy of the proposed estimation procedure.     

Estimation of random regression parameters

The problem of the best linear unbiased estimation (BLUE) of random regression parameters is considered. It is proved that increasing informations about the mean value of the parameters both extend the class of estimable linear functionals and improve on the estimation. In all investigated cases the uniqueness of BLUE is proved. In the case of known mean values the BLUE is shown to be numerically equivalent with the MMSEE almost everywhere. A numerical example shows the improvements of BLUE due to increasing informations about the mean values of the parameters.     

Set-up uncertainty during postmastectomy radiotherapy with Segmented Photon Beams Technique

Aim

To verify the reproducibility of patients irradiated after mastectomy on the immobilization system designed and manufactured for our hospital and to compare the Internal Protocol (IP) with the modified-No Action Level Protocol.

Background

Application of forward IMRT techniques requires a good reproducibility of patient positioning. To minimize the set-up error, an effective immobilization system is important.

Materials and methods

The study was performed for two groups of 65 each. In the first group, portal images for anterior field were taken in 1–3 fractions and, subsequently, three times a week. In this group, the mNAL protocol was used. In the second group, the IP was used. The portal images from the anterior field and from the gantry 0 were taken during the 1–3 and 10 fractions. In both groups, image registration was performed off-line. For each group the systematic and random errors and PTV margin were calculated.

Results

In the first group the value of the population systematic errors and random errors were 1.6 ± 1.6 mm for the left–right, and 1.5 ± 1.7 mm for the cranial–caudal directions, respectively, 1.7 ± 1.3 mm, and 1.9 ± 1.3 mm for the second group. The PTV margins for the left–right and cranial–caudal directions were 5.1 and 4.9 mm for the first group and 5.4 and 6.4 mm for the second group.

Conclusions

For patients immobilized with our support device treated according to the mNAL protocol or IP, a good set-up reproducibility was obtained. Implementation of IP limits the number of required images.     

Estimation of regression models under linear restrictions

The variance-covariance matrices of restricted regression and mixed regression estimators are compared and the consequences of introducing variability in the restrictions are examined.     

Comparative methods based on species mean values

Comparative methods that use simple linear regression based on species mean values introduce three difficulties with respect to the standard regression model. First, species values may not be independent because they form part of a hierarchically structured phylogeny. Second, variation about the regression line includes two sources of error: 'biological error' due to deviations of the true species mean values from the regression line and sampling error associated with the estimation of these mean values [B. Riska, Am. Natural. 138 (1991) 283]. Third, sampling error in the independent variable results in an attenuated estimate of the regression slope. We consider estimation and hypothesis testing using two statistical models which explicitly justify the use of the species mean values, without the need to account for phylogenetic relationships. The first (random-effects) is based on an evolutionary model whereby species evolve to fill a bivariate normal niche space, and the second (fixed-effects) is concerned with describing a relationship among the particular species included in a study, where the only source of error is in the estimation of species mean values. We use a modification of the maximum-likelihood method to obtain an unbiased estimate of the regression slope. For three real datasets we find a close correspondence between this slope and that obtained by simply regressing the species mean values on each other. In the random effects model, the P-value also approximates that based on the regression of species mean values. In the fixed effects model, the P-value is typically much lower. Simulated examples illustrate that the maximum-likelihood approach is useful when the accuracy in estimating the species mean values is low, but the traditional method based on a regression of the species mean values may often be justified provided that the evolutionary model can be justified.     

Approximating selective sweeps

The fixation of advantageous mutations in a population has the effect of reducing variation in the DNA sequence near that mutation. Kaplan et al. (1989) used a three-phase simulation model to study the effect of selective sweeps on genealogies. However, most subsequent work has simplified their approach by assuming that the number of individuals with the advantageous allele follows the logistic differential equation. We show that the impact of a selective sweep can be accurately approximated by a random partition created by a stick-breaking process. Our simulation results show that ignoring the randomness when the number of individuals with the advantageous allele is small can lead to substantial errors.