Homosexual role separation and AIDS epidemics: Insights from elementary models

Simple models of a closed homosexual population are developed to explore the effect of differentiation of roles in anal intercourse on the size of an AIDS epidemic. Preferential and random mixing among the sex‐role subgroups are modeled via a concept of partnership‐formation rates for pairs of individuals. Models of differing mixing assumptions are compared via a concept of reference reproductive rate. Under the assumption of no risk associated with insertive anal intercourse, explicit epidemic thresholds are determined; epidemic intensity increases with increasing size of the dual‐role (insertive and receptive) subpopulation. Other results indicate that there is a threshold for reproductive rates which determines whether or not random mixing yields a more severe epidemic than a form of segregated mixing, and that for fixed epidemiological conditions, a certain level of like‐with‐like preference, rather than random mixing, yields a worst‐case scenario.     

Sensitivity analysis approaches to high-dimensional screening problems at low sample size

Sensitivity analysis is an essential tool in the development of robust models for engineering, physical sciences, economics and policy-making, but typically requires running the model a large number of times in order to estimate sensitivity measures. While statistical emulators allow sensitivity analysis even on complex models, they only perform well with a moderately low number of model inputs: in higher dimensional problems they tend to require a restrictively high number of model runs unless the model is relatively linear. Therefore, an open question is how to tackle sensitivity problems in higher dimensionalities, at very low sample sizes. This article examines the relative performance of four sampling-based measures which can be used in such high-dimensional nonlinear problems. The measures tested are the Sobol' total sensitivity indices, the absolute mean of elementary effects, a derivative-based global sensitivity measure, and a modified derivative-based measure. Performance is assessed in a ‘screening’ context, by assessing the ability of each measure to identify influential and non-influential inputs on a wide variety of test functions at different dimensionalities. The results show that the best-performing measure in the screening context is dependent on the model or function, but derivative-based measures have a significant potential at low sample sizes that is currently not widely recognised.     

Economic statistical design of a multivariate control chart under a Burr XII shock model with multiple assignable causes

Control charts show the distinction between the random and assignable causes of variation in a process. The real process may be affected by many characteristics and several assignable causes. Therefore, the economic statistical design of multiple control chart under Burr XII shock model with multiple assignable causes can be an appropriate candidate model. In this paper, we develop a cost model based on the optimization of the average cost per unit of time. Indeed, the cost model under the influence of a single match case assignable cause and multiple assignable causes under a same cost and time parameters were compared. Besides, a sensitivity analysis was also presented in which the changeability of loss-cost and design parameters were evaluated based on the changes in cost, time and Burr XII distribution parameters.     

物理系学生和数学系学生思维差异分析与普物教学

物理学习与数学有着密切的联系。结合具体的教学例子,分析了物理系学生与数学系学生在普物学习的过程中存在的思维差异,认为应注意到这些差异,对不同学生应采用不同的教学方法,以提高教学质量。     

Using pilot study information to increase efficiency in clinical trials

It is often necessary to conduct a pilot study to determine the sample size required for a clinical trial. Due to differences in sampling environments, the pilot data are usually discarded after sample size calculation. This paper tries to use the pilot information to modify the subsequent testing procedure when a two-sided t<math altimg="si31.gif" overflow="scroll">tmath>-test or a regression model is used to compare two treatments. The new test maintains the required significance level regardless of the dissimilarity between the pilot and the target populations, but increases the power when the two are similar. The test is constructed based on the posterior distribution of the parameters given the pilot study information, but its properties are investigated from a frequentist's viewpoint. Due to the small likelihood of an irrelevant pilot population, the new approach is a viable alternative to the current practice.     

Testing homogeneity in discrete mixtures

This paper introduces W-tests for assessing homogeneity in mixtures of discrete probability distributions. A W-test statistic depends on the data solely through parameter estimators and, if a penalized maximum likelihood estimation framework is used, has a tractable asymptotic distribution under the null hypothesis of homogeneity. The large-sample critical values are quantiles of a chi-square distribution multiplied by an estimable constant for which we provide an explicit formula. In particular, the estimation of large-sample critical values does not involve simulation experiments or random field theory. We demonstrate that W-tests are generally competitive with a benchmark test in terms of power to detect heterogeneity. Moreover, in many situations, the large-sample critical values can be used even with small to moderate sample sizes. The main implementation issue (selection of an underlying measure) is thoroughly addressed, and we explain why W-tests are well-suited to problems involving large and online data sets. Application of a W-test is illustrated with an epidemiological data set.     

Prediction intervals for general balanced linear random models

The main interest of prediction intervals lies in the results of a future sample from a previously sampled population. In this article, we develop procedures for the prediction intervals which contain all of a fixed number of future observations for general balanced linear random models. Two methods based on the concept of a generalized pivotal quantity (GPQ) and one based on ANOVA estimators are presented. A simulation study using the balanced one-way random model is conducted to evaluate the proposed methods. It is shown that one of the two GPQ-based and the ANOVA-based methods are computationally more efficient and they also successfully maintain the simulated coverage probabilities close to the nominal confidence level. Hence, they are recommended for practical use. In addition, one example is given to illustrate the applicability of the recommended methods.