Estimating household structure in ancient China by using historical data: a latent class analysis of partially missing patterns

Summary.  Social data often contain missing information. The problem is inevitably severe when analysing historical data. Conventionally, researchers analyse complete records only. Listwise deletion not only reduces the effective sample size but also may result in biased estimation, depending on the missingness mechanism. We analyse household types by using population registers from ancient China (618–907 AD) by comparing a simple classification, a latent class model of the complete data and a latent class model of the complete and partially missing data assuming four types of ignorable and non-ignorable missingness mechanisms. The findings show that either a frequency classification or a latent class analysis using the complete records only yielded biased estimates and incorrect conclusions in the presence of partially missing data of a non-ignorable mechanism. Although simply assuming ignorable or non-ignorable missing data produced consistently similarly higher estimates of the proportion of complex households, a specification of the relationship between the latent variable and the degree of missingness by a row effect uniform association model helped to capture the missingness mechanism better and improved the model fit.     

Improving Convergence of the HastingsMetropolis Algorithm with an Adaptive Proposal

The HastingsMetropolis algorithm is a general MCMC method for sampling from a density known up to a constant. Geometric convergence of this algorithm has been proved under conditions relative to the instrumental (or proposal) distribution. We present an inhomogeneous HastingsMetropolis algorithm for which the proposal density approximates the target density, as the number of iterations increases. The proposal density at the n th step is a non-parametric estimate of the density of the algorithm, and uses an increasing number of i.i.d. copies of the Markov chain. The resulting algorithm converges (in n ) geometrically faster than a HastingsMetropolis algorithm with any fixed proposal distribution. The case of a strictly positive density with compact support is presented first, then an extension to more general densities is given. We conclude by proposing a practical way of implementation for the algorithm, and illustrate it over simulated examples.     

Bayesian analysis of outlier problems using divergence measures

A Bayesian approach is presented for detecting influential observations using general divergence measures on the posterior distributions. A sampling-based approach using a Gibbs or Metropolis-within-Gibbs method is used to compute the posterior divergence measures. Four specific measures are proposed, which convey the effects of a single observation or covariate on the posterior. The technique is applied to a generalized linear model with binary response data, an overdispersed model and a nonlinear model. An asymptotic approximation using Laplace method to obtain the posterior divergence is also briefly discussed.     

A multivariate zero-inflated binomial model for the analysis of correlated proportional data

In this paper, a new multivariate zero-inflated binomial (MZIB) distribution is proposed to analyse the correlated proportional data with excessive zeros. The distributional properties of purposed model are studied. The Fisher scoring algorithm and EM algorithm are given for the computation of estimates of parameters in the proposed MZIB model with/without covariates. The score tests and the likelihood ratio tests are derived for assessing both the zero-inflation and the equality of multiple binomial probabilities in correlated proportional data. A limited simulation study is performed to evaluate the performance of derived EM algorithms for the estimation of parameters in the model with/without covariates and to compare the nominal levels and powers of both score tests and likelihood ratio tests. The whitefly data is used to illustrate the proposed methodologies.     

Bayesian analysis of human movement curves

Summary.  We consider the Bayesian analysis of human movement data, where the subjects perform various reaching tasks. A set of markers is placed on each subject and a system of cameras records the three-dimensional Cartesian co-ordinates of the markers during the reaching movement. It is of interest to describe the mean and variability of the curves that are traced by the markers during one reaching movement, and to identify any differences due to covariates. We propose a methodology based on a hierarchical Bayesian model for the curves. An important part of the method is to obtain identifiable features of the movement so that different curves can be compared after temporal warping. We consider four landmarks and a set of equally spaced pseudolandmarks are located in between. We demonstrate that the algorithm works well in locating the landmarks, and shape analysis techniques are used to describe the posterior distribution of the mean curve. A feature of this type of data is that some parts of the movement data may be missing—the Bayesian methodology is easily adapted to cope with this situation.     

互连网络拓扑优化设计

论述了互连网络拓扑优化设计问题,建立了必要的数学模型,该数学模型是一个非线性组合优化问题,它属于NP—完备类问题。采取拉格朗日松弛法、次梯度迭代算法和启发式算法,得出最优下确界和结论。     

Proof of Toft's Conjecture: Every Graph Containing No Fully Odd K4 is 3-Colorable

A fully odd K₄ is a subdivision of K₄ such that each of the six edges of the K₄ is subdivided into a path of odd length. In 1974, Toft conjectured that every graph containing no fully odd K₄ can be vertex-colored with three colors. The purpose of this paper is to prove Toft's conjecture.     

On-Line Scheduling of Two-Machine Open Shops Where Jobs Arrive Over Time

We investigate the problem of on-line scheduling two-machine open shops with the objective of minimizing the makespan.Jobs arrive independently over time, and the existence of a job is not known until its arrival. In the clairvoyant on-line model, the processing requirement of every job becomes fully known at the arrival of the job, while inthe non-clairvoyant on-line model, this processing requirement is notknown until the job is processed and completed.In both models, scheduling of a job is irrevocable.We study the two-machine open shop problem for both models in the preemptive and in the non-preemptive version. For each of the four variants, we provide an algorithm that is best possible with respect to the worst-case performance. In the clairvoyant on-line model, the best worst-case performance ratios are 5/4 (preemptive) and 3/2 (non-preemptive), and in the non-clairvoyant on-line model, they are 3/2 (preemptive and non-preemptive).     

A Note on Inconsistency of NPMLE of the Distribution Function from Left Truncated and Case I Interval Censored Data

We show that under reasonable conditions the nonparametric maximum likelihood estimate (NPMLE) of the distribution function from left-truncated and case 1 interval-censored data is inconsistent, in contrast to the consistency properties of the NPMLE from only left-truncated data or only interval-censored data. However, the conditional NPMLE is shown to be consistent. Numerical examples are provided to illustrate their finite sample properties.     

Modelling Variability in the Branching Structure of Strawberry Inflorescences

The branching structure of inflorescences of the cultivated strawberry ( Fragaria × ananassa Duch.) is very variable. This paper demonstrates that some aspects of this variability are well described by a simple stochastic model of branching that has two adjustable parameters. The model is shown to provide a good fit to data from a set of almost 700 inflorescences of the cultivar Elsanta, collected over two successive years. For one parameter the maximum likelihood estimator is a moment estimator which is fully efficient even if the detailed branching structure of the inflorescences is not recorded. This parameter provides a convenient summary of branching vigour. The maximum likelihood estimator of the second parameter must be determined iteratively and can be quite inefficient unless the full branching structure is recorded. The model demonstrates that branching structure is affected by the order in which inflorescences emerge on the plant.