An Application of Markov Chain Analysis to the Game of Squash*

If the score in a squash game is tied late in the game, one player has a choice of how many additional points (from a prespecified set of possibilities) are to be played to determine the winner. This paper constructs a Markov chain model of the situation and solves for the optimal strategy. Expressions for the optimal strategy are obtained with a symbolic algebra computer package. Results are given for both international and American scoring systems. The model and analysis are very suitable for educational purposes. The resulting Markov chain is small enough that it can be easily presented in a classroom setting, yet the model is sufficiently complex that algebraic manipulation is nearly hopeless. The final results illustrate the power of the combination of mathematical and computer modeling applied to a problem of practical interest.     

动画作品对青少年价值观的影响研究

在发达的多媒体时代,青少年价值观教育需要更为合适的形式,而动画作品或多或少影响着少年儿童,对他们的价值观与行为产生影响。借助手段-目的链理论（MEC）,采用硬性阶梯与焦点小组访谈法,对290名青少年进行调查,分析了动画作品对青少年的影响。研究提取了23个要素作为动画的属性层、结果层及价值层并构建了三者间的综合关联矩阵,绘制了动画作品影响青少年的层级价值图,探讨动画作品应怎样持续发挥其价值观引导作用。     

电信设备制造商全球价值链升级路径分析——以华为技术有限公司为例

随着经济全球化进程加速,我国电信设备制造商开始国际化进程,嵌入全球价值链及全球价值链下企业升级问题显得尤为重要.华为公司是我国通信制造业国际化的先锋企业,其通过技术创新与研发,向全球电信价值链高端不断攀升,通过向终端转型带动整体价值链链条升级,这使华为公司逐渐成为全球第二大电信设备制造商.对于我国其他设备商来说,华为的成功具有重要借鉴意义.     

On hysteretic vector autoregressive model with applications

This paper proposes a new hysteretic vector autoregressive (HVAR) model in which the regime switching may be delayed when the hysteresis variable lies in a hysteresis zone. We integrate an adapted multivariate Student-t distribution from amending the scale mixtures of normal distributions. This HVAR model allows for a higher degree of flexibility in the degrees of freedom for each time series. We use the proposed model to test for a causal relationship between any two target time series. Using posterior odds ratios, we overcome the limitations of the classical approach to multiple testing. Both simulated and real examples herein help illustrate the suggested methods. We apply the proposed HVAR model to investigate the causal relationship between the quarterly growth rates of gross domestic product of United Kingdom and United States. Moreover, we check the pairwise lagged dependence of daily PM2.5 levels in three districts of Taipei.     

Bayesian inference for stable Lévy–driven stochastic differential equations with high‐frequency data

In this paper, we consider parametric Bayesian inference for stochastic differential equations driven by a pure‐jump stable Lévy process, which is observed at high frequency. In most cases of practical interest, the likelihood function is not available; hence, we use a quasi‐likelihood and place an associated prior on the unknown parameters. It is shown under regularity conditions that there is a Bernstein–von Mises theorem associated to the posterior. We then develop a Markov chain Monte Carlo algorithm for Bayesian inference, and assisted with theoretical results, we show how to scale Metropolis–Hastings proposals when the frequency of the data grows, in order to prevent the acceptance ratio from going to zero in the large data limit. Our algorithm is presented on numerical examples that help verify our theoretical findings.     

Efficient Bayesian inference in generalized inverse gamma processes for stochastic volatility

This paper develops a novel and efficient algorithm for Bayesian inference in inverse Gamma stochastic volatility models. It is shown that by conditioning on auxiliary variables, it is possible to sample all the volatilities jointly directly from their posterior conditional density, using simple and easy to draw from distributions. Furthermore, this paper develops a generalized inverse gamma process with more flexible tails in the distribution of volatilities, which still allows for simple and efficient calculations. Using several macroeconomic and financial datasets, it is shown that the inverse gamma and generalized inverse gamma processes can greatly outperform the commonly used log normal volatility processes with Student’s t errors or jumps in the mean equation.     

具有延误休假的一个基本可修系统的可靠性分析

本文讨论了由两个同型部件和一个修理工组成的可修系统。假定修理工空闲时进行延误休假。部件的修理时间和修理工的假期均服从一般分布，休假前的延误期为指数分布。我们求得了这个系统的可用度、可靠度和故障频度。作为特例，我们还讨论了修理工进行不延误休假的情况。     

我国区域经济差距的空间演变趋势及其成因

文章采用空间马尔科夫链方法分析了我国区域差距和经济发展的空间效应及演变趋势,发现地理背景对经济类型转移具有显著影响,区域经济类型不会发生明显的跃迁,经济增长存在空间相关性和路径依赖性。然后,利用Kernel密度分布法提供了同时考察经济增长及区域差距的新分析框架,从经济增长分布演进的视角,分析了我国区域经济差距的原因。研究结果显示,中国经济差距扩散的动力来源于效率改进而非要素投入。     

脑-机接口中新的脑电数据分类方法

根据自发脑电的特点,将HMM-AR模型算法运用到脑电状态的分类中,证明它是一种非常有用的分析脑-机接口方法。将Laplacian filter、ICA和HMM-AR方法相结合,用想象左右手运动的BCI数据进行识别,得到了很好的分类结果,有效地区分脑电中运动与非运动两种状态。该算法能够在运动开始后1 s内检验到脑电信号的变化,从而证明了该算法在BCI的实用性,达到了良好的识别效果。     

带有马尔可夫调制和跳的随机微分延迟方程Euler方法的强相合性

本文主要研究了下列形式的随机微分延迟方程：dX（t） =f（X（t） ,X（t -τ（t） ） ,r（t） ）dt ＋g（X（t） ,X（t -τ（t） ） ,r（t） ）dW（t） ＋h（X（t） ,X（t -τ（t） ）, r（t） ）dN（t） 0≤t≤T.考虑了时间延迟．r（t）为变量，Euler方法数值解；给出并且证明了Euler方法的强相合性定理，即Euler方法数值解均方意义下局部收敛于精确解．