Domains of convergence for the EM algorithm: a cautionary tale in a location estimation problem

The EM algorithm is a popular method for maximizing a likelihood in the presence of incomplete data. When the likelihood has multiple local maxima, the parameter space can be partitioned into domains of convergence, one for each local maximum. In this paper we investigate these domains for the location family generated by the t-distribution. We show that, perhaps somewhat surprisingly, these domains need not be connected sets. As an extreme case we give an example of a domain which consists of an infinite union of disjoint open intervals. Thus the convergence behaviour of the EM algorithm can be quite sensitive to the starting point.     

情商在体育教学中的作用

学校体育教学的现状与时代的要求尚有一定距离,体育教学的改革势在必行。阐述情商EQ在体育教学中所起的作用。     

Uncertain Numbers and Uncertainty in the Selection of Input Distributions—Consequences for a Probabilistic Risk Assessment of Contaminated Land

Risks from exposure to contaminated land are often assessed with the aid of mathematical models. The current probabilistic approach is a considerable improvement on previous deterministic risk assessment practices, in that it attempts to characterize uncertainty and variability. However, some inputs continue to be assigned as precise numbers, while others are characterized as precise probability distributions. Such precision is hard to justify, and we show in this article how rounding errors and distribution assumptions can affect an exposure assessment. The outcome of traditional deterministic point estimates and Monte Carlo simulations were compared to probability bounds analyses. Assigning all scalars as imprecise numbers (intervals prescribed by significant digits) added uncertainty to the deterministic point estimate of about one order of magnitude. Similarly, representing probability distributions as probability boxes added several orders of magnitude to the uncertainty of the probabilistic estimate. This indicates that the size of the uncertainty in such assessments is actually much greater than currently reported. The article suggests that full disclosure of the uncertainty may facilitate decision making in opening up a negotiation window. In the risk analysis process, it is also an ethical obligation to clarify the boundary between the scientific and social domains.     

Analytical approximations for iterated bootstrap confidence intervals

Standard algorithms for the construction of iterated bootstrap confidence intervals are computationally very demanding, requiring nested levels of bootstrap resampling. We propose an alternative approach to constructing double bootstrap confidence intervals that involves replacing the inner level of resampling by an analytical approximation. This approximation is based on saddlepoint methods and a tail probability approximation of DiCiccio and Martin (1991). Our technique significantly reduces the computational expense of iterated bootstrap calculations. A formal algorithm for the construction of our approximate iterated bootstrap confidence intervals is presented, and some crucial practical issues arising in its implementation are discussed. Our procedure is illustrated in the case of constructing confidence intervals for ratios of means using both real and simulated data. We repeat an experiment of Schenker (1985) involving the construction of bootstrap confidence intervals for a variance and demonstrate that our technique makes feasible the construction of accurate bootstrap confidence intervals in that context. Finally, we investigate the use of our technique in a more complex setting, that of constructing confidence intervals for a correlation coefficient.     

论《周易》中圣人崇拜思想及影响

《周易》的圣人崇拜思想 ,既有积极作用 ,更多的是消极作用 ,必须在新时代加以转换     

科学执政、民主执政中的依法执政基本途径

依法执政或依法行政,作为执政方式最为直接、最为具体的基本实践环节或途径,在相当范围内反映着科学执政、民主执政的实现程度。这取决于《行政许可法》不打折扣地坚决实施,政府的依法执政职能方式从重管制向重服务转变;职能范围从“全能”向“有限”回归;职能性质由“专断”走向真正“民主”;职能习惯从主观随意转向严格的法治。     

二项式函数在组合恒等式证明中的应用

一些恒等式在函数论、组合数学、解析数论等学科的研究领域中极为重要。以二项式作为生成函数,给出了几个组合恒等式证明。     

对区域经济增长路径选择的实证分析:以中部五省为例

通过采用C-D生产函数对中部五省经济增长的有关因素进行分析后认为,对中部五省经济增长影响较大的因素依次为:城市化水平、劳动就业状况、对外开放程度、固定资产投资规模。因此,推进城市化进程和促进劳动就业应成为实现中部地区经济增长的主要路径和制定经济政策的首要切入点。     

Semiparametric linear transformation models for current status data

Current status data arise when the death of every subject in a study cannot be determined precisely, but is known only to have occurred before or after a random monitoring time. The authors discuss the analysis of such data under semiparametric linear transformation models for which they propose a general inference procedure based on estimating functions. They determine the properties of the estimates they propose for the regression parameters of the model and illustrate their technique using tumorigenicity data.     

西北少数民族地区乡村初级群体及其功能分析

社会群体是人们社会生活中的具体单位,社会群体生活是人们的基本生活方式,因此,群体就成为社会学研究的主要组成部分,社会学如此,民族社会学更如此。处于转型期的西北民族乡村社会,社会群体特别是初级群体依然扮演着极其重要的角色。对其进行功能分析有助于深化对它们的认识。