Standard errors for EM estimation

The EM algorithm is a popular method for computing maximum likelihood estimates. One of its drawbacks is that it does not produce standard errors as a by-product. We consider obtaining standard errors by numerical differentiation. Two approaches are considered. The first differentiates the Fisher score vector to yield the Hessian of the log-likelihood. The second differentiates the EM operator and uses an identity that relates its derivative to the Hessian of the log-likelihood. The well-known SEM algorithm uses the second approach. We consider three additional algorithms: one that uses the first approach and two that use the second. We evaluate the complexity and precision of these three and the SEM in algorithm seven examples. The first is a single-parameter example used to give insight. The others are three examples in each of two areas of EM application: Poisson mixture models and the estimation of covariance from incomplete data. The examples show that there are algorithms that are much simpler and more accurate than the SEM algorithm. Hopefully their simplicity will increase the availability of standard error estimates in EM applications. It is shown that, as previously conjectured, a symmetry diagnostic can accurately estimate errors arising from numerical differentiation. Some issues related to the speed of the EM algorithm and algorithms that differentiate the EM operator are identified.     

Slow‐fast dynamics in a model of population and resource growth

Models of the interaction of population, the economy, and the environment often contain nonlinear functional relationships and variables that move at different speeds. These properties foster apparent unpredictabilities in system behaviour. Using a simple deterministic model of demographic, economic and environmental interactions we illustrate the usefulness of geometric singular perturbation theory in environmental population economics. In contrast to local stability analysis, the theory of slow‐fast dynamics helps to gain new insights into the global behaviour of the system. In particular, the knowledge of the basins of attraction of the stationary states enables one to determine the regions of sustainable future paths of resources and population.     

湖湘道教隐逸文学视阈下慢综艺旨趣 ——以《向往的生活》为例

湖湘道教隐逸文学是中国传统文化的一个重要组成部分,以展现隐士的生活状态与精神世界为核心,表达创作者对质朴平和心境的向往之情。在慢综艺《向往的生活》中,大自然的清纯明静、“出世”乡村生活的恬淡悠然、人心的美好本真,闪烁着湖湘道教隐逸思想的光芒。在快节奏的城市生活压力下,人们更加向往简单舒适的乡村田园生活。以《向往的生活》为代表的慢综艺,与漂泊在都市霓虹灯下的人的心理需求相吻合,提升了综艺节目的文化质感,传达出人与大自然、人与社会、人与人和谐共生的传统文化内涵。     

试论慢设计之"慢"

慢设计是为了倡导"慢"生活,创造可持续的现在与未来。慢设计理论目前还处于初步发展阶段,慢设计的"慢"还只是一个十分抽象的且正在发展中的概念。而"快"与快设计对人类可持续发展的负面影响引发了我们时"慢"和慢设计的深层思考,通过了解"慢"在慢设计理论中的含义以及其概念的延伸能够使我们更好地了解慢设计和它对可持续发展的积极作用。     

农民收入增长迟缓成因探析

近年来,我国农民收入增长不稳定、农民收入差距扩大、农民的现金收入减少,从而制约着经济发展和社会的稳定。农民收入增长迟缓的原因是多方面的,既有农民自身素质和思想观念的原因,又有农业政策和农村经济体制的原因。我们应采取综合措施,从多方面促进农民收入的快速增长。     

具有可变几何喷嘴的增压器轴流涡轮热力计算方法

本文提出具有可变几何喷嘴的增压器轴流涡轮热力计算方法。引入三个脉冲系数将脉冲涡轮按等压涡轮计算。给定通流部分尺寸,利用可变几何喷嘴来满足所驱动压气机和涡轮的配合。考虑各部实际损失,采用吴仲华燃气热力性质表迭代计算求出反动度、喷嘴出气角和喉口面积。可给定废气初温时迭代所需的初压或给定初压时迭代所需的初温,并算出涡轮当量通流面积。计算结果表明迭代计算是收敛的,算出的喷嘴喉口面积与实际相符。     

钢琴学习之我见

我们进行钢琴演奏教学时,往往会忽视对"基础"的巩固,钢琴演奏需要很强的演奏技巧,因此,将"温故而知新"的古训发扬下去是很有必要的,任何一位钢琴大师的成长都伴随着刻苦的训练,他们的成功都是经过长期不懈努力才取得的。     

从文化语境对等角度看许渊冲译《声声慢》

中国古典诗词翻译与文化语境密不可分,译者要充分解读原文语境并考虑译文读者所属文化语境,对原文进行适当增益、删减或创造性改动,以便译语读者在译语文化语境下能和原文读者一样,获得美的感受。文章通过赏析许渊冲所译《声声慢》发现,为了达到原文与译文在不同文化语境中的功能对等,译者在翻译中可以采取变通手段,只要译文与原文在不同文化语境中达到相同的审美效果,就是好译文。