On the equivalence of two approaches to simplicity in the analysis of block designs and some related results

Two seemingly different approaches to simplicity in the analysis of connected block designs, and their relationship to the concepts of balance are discussed.     

Optimality and bias of some interpolation and extrapolation designs

We consider interpolation and extrapolation designs with controlled bias. A consistent estimate of an upper bound of the bias is presented. The estimate of some extrapolated value is obtained in a two-stage procedure. The first one provides an estimate of some interpolated value. The second one uses a Taylor expansion around this point. This procedure yields a new type of designs. We discuss their optimality properties with respect to the variance and the bias.     

Multivariate inverse Gaussian distribution as a limit of multivariate waiting time distributions

Multivariate inverse Gaussian distribution proposed by Minami [2003. A multivariate extension of inverse Gaussian distribution derived from inverse relationship. Commun. Statist. Theory Methods 32(12), 2285–2304] was derived through multivariate inverse relationship with multivariate Gaussian distributions and characterized as the distribution of the location at a certain stopping time of a multivariate Brownian motion. In this paper, we show that the multivariate inverse Gaussian distribution is also a limiting distribution of multivariate Lagrange distributions, which is a family of waiting time distributions, under certain conditions.     

Considerations on group-wise identical designs for linear mixed models

We consider a general class of mixed models, where the individual parameter vector is composed of a linear function of the population parameter vector plus an individual random effects vector. The linear function can vary for the different individuals. We show that the search for optimal designs for the estimation of the population parameter vector can be restricted to the class of group-wise identical designs, i.e., for each of the groups defined by the different linear functions only one individual elementary design has to be optimized. A way to apply the result to non-linear mixed models is described.     

On the construction of a class of efficient row-column designs

In this paper a method for the construction of a class of row-column designs with good statistical properties and high efficiency is presented. The class of designs produced is shown to exhibit balance, orthogonality and adjusted orthogonality. The efficiencies of these designs are investigated in detail, and they are shown to be very high, and possibly maximal in some cases.     

Bayesian mixture modeling for spatial Poisson process intensities,with applications to extreme value analysis

We propose a method for the analysis of a spatial point pattern, which is assumed to arise as a set of observations from a spatial nonhomogeneous Poisson process. The spatial point pattern is observed in a bounded region, which, for most applications, is taken to be a rectangle in the space where the process is defined. The method is based on modeling a density function, defined on this bounded region, that is directly related with the intensity function of the Poisson process. We develop a flexible nonparametric mixture model for this density using a bivariate Beta distribution for the mixture kernel and a Dirichlet process prior for the mixing distribution. Using posterior simulation methods, we obtain full inference for the intensity function and any other functional of the process that might be of interest. We discuss applications to problems where inference for clustering in the spatial point pattern is of interest. Moreover, we consider applications of the methodology to extreme value analysis problems. We illustrate the modeling approach with three previously published data sets. Two of the data sets are from forestry and consist of locations of trees. The third data set consists of extremes from the Dow Jones index over a period of 1303 days.     

钼酸钙晶体中点缺陷的电子结构研究

运用以密度泛函理论为基础的相对论性离散变分方法(DV-Xα),模拟计算了完整的和含氧空位的钼酸钙(CaMoO_4)晶体的电子结构,得到了含有F、F~ 心的CaMoO_4晶体电子态密度分布以及它们可能产生的光学跃迁模式.计算结果表明,含F、F~ 心的CaMoO_4晶体的禁带宽度明显变窄,F、F~ 心的能级出现在禁带中,利用过渡态理论计算得到其向Mo的4 d轨道发生光学跃迁,跃迁能量值分别为1.93,2.03 eV.利用提拉法生长的CaMoO_4晶体呈现蓝色的本质原因是F、F~ 心在黄红区产生比较强的吸收.     

An alternative estimator for multiple characteristics in PPS sampling

The problem considered relates to large-scale sample surveys. A new estimator of population total for the characteristics that are poorly correlated with the selection probabilities has been developed for the PPSWR sampling scheme. The relative efficiency of the proposed estimator has been studied under a super-population model. A numerical investigation into the performance of the estimator has also been made.     

On Tiku's robust procedure — a Bayesian insight

Tiku's robust procedure for testing mean and variance from nonnormal universe is examined from the Bayesian viewpoint. The posterior distribution of the scale parameter is derived and then approximated by a Laguerre polynomial expansion while the posterior distribution of the location parameter is approximated by a linear combination of t-distributions. For the example with Darwin's data, the approximations appear to be extremely good.     

Optimal discrimination designs for exponential regression models

We investigate optimal designs for discriminating between exponential regression models of different complexity, which are widely used in the biological sciences; see, e.g., Landaw [1995. Robust sampling designs for compartmental models under large prior eigenvalue uncertainties. Math. Comput. Biomed. Appl. 181–187] or Gibaldi and Perrier [1982. Pharmacokinetics. Marcel Dekker, New York]. We discuss different approaches for the construction of appropriate optimality criteria, and find sharper upper bounds on the number of support points of locally optimal discrimination designs than those given by Caratheodory's Theorem. These results greatly facilitate the numerical construction of optimal designs. Various examples of optimal designs are then presented and compared to different other designs. Moreover, to protect the experiment against misspecifications of the nonlinear model parameters, we adapt the design criteria such that the resulting designs are robust with respect to such misspecifications and, again, provide several examples, which demonstrate the advantages of our approach.