Rényi entropy of m-generalized order statistics

Abstract

Characterizing relations via Rényi entropy of m-generalized order statistics are considered along with examples and related stochastic orderings. Previous results for common order statistics are included.     

从主权国家的兴衰看权力博弈形态的转型

传统的国际关系理论,无论是现实主义、自由主义、建构主义还是科学行为主义理论,都是把主权国家抽象成一个统一的国际关系行为体。这一行为主体有一致的利益,也自然要有一致的对外政策目标和手段。在20世纪,尤其是在两次世界大战和冷战期间,这一概念抽象是非常准确的。但冷战结束以后,尤其是进入21世纪以后,这一概念抽象逐渐与国际关系的现实相违背。一方面,国家综合实力并不能直接转化为具体领域的竞争优势;另一方面,很多国家,包括超级大国在内,其对外政策的主要阻力可能不是所谓的竞争对手,而是其国内不同的利益集团。这导致传统的国际关系理论,从假设到概念和推理层面,都已经无法解释和预测今天的世界,而权力小博弈理论可以为认识多元复杂互动博弈时代的国际关系提供一个新的解释框架。     

Who Should Pay for Interdependent Risk? Policy Implications for Security Interdependence Among Airports

We study interdependent risks in security, and shed light on the economic and policy implications of increasing security interdependence in presence of reactive attackers. We investigate the impact of potential public policy arrangements on the security of a group of interdependent organizations, namely, airports. Focusing on security expenditures and costs to society, as assessed by a social planner, to individual airports and to attackers, we first develop a game-theoretic framework, and derive explicit Nash equilibrium and socially optimal solutions in the airports network. We then conduct numerical experiments mirroring real-world cyber scenarios, to assess how a change in interdependence impact the airports' security expenditures, the overall expected costs to society, and the fairness of security financing. Our study provides insights on the economic and policy implications for the United States, Europe, and Asia.     

Confidence intervals,significance values,maximum likelihood estimates,etc. sharpened into Occam’s razors

Abstract

Confidence sets, p values, maximum likelihood estimates, and other results of non-Bayesian statistical methods may be adjusted to favor sampling distributions that are simple compared to others in the parametric family. The adjustments are derived from a prior likelihood function previously used to adjust posterior distributions.     

Security Investment in Contagious Networks

Security of the systems is normally interdependent in such a way that security risks of one part affect other parts and threats spread through the vulnerable links in the network. So, the risks of the systems can be mitigated through investments in the security of interconnecting links. This article takes an innovative look at the problem of security investment of nodes on their vulnerable links in a given contagious network as a game‐theoretic model that can be applied to a variety of applications including information systems. In the proposed game model, each node computes its corresponding risk based on the value of its assets, vulnerabilities, and threats to determine the optimum level of security investments on its external links respecting its limited budget. Furthermore, direct and indirect nonlinear influences of a node's security investment on the risks of other nodes are considered. The existence and uniqueness of the game's Nash equilibrium in the proposed game are also proved. Further analysis of the model in a practical case revealed that taking advantage of the investment effects of other players, perfectly rational players (i.e., those who use the utility function of the proposed game model) make more cost‐effective decisions than selfish nonrational or semirational players.     

农业投入中政府与农户的博弈分析

农业投入状况关系着农业生产和农村经济的发展。目前农业投入不足已成为制约我国整体经济发展的“瓶颈”。在是否增加农业投入的问题上,政府与农户之间存在着一种博弈关系。通过农业投入不足的现状考察,用博弈的方法阐释农业投入不足的原因,提出加大农业投入的几点对策。     

几类全微分方程问题的求解定理

利用全微分方程的条件，给出一类微分方程的积分因子及通解公式，得出一类全微分方程中未知函数所满足的二阶线性微分方程，获得未知函数及全微分方程的通解。     

On the Convergence of the Monte Carlo Maximum Likelihood Method for Latent Variable Models

While much used in practice, latent variable models raise challenging estimation problems due to the intractability of their likelihood. Monte Carlo maximum likelihood (MCML), as proposed by Geyer & Thompson (1992 ), is a simulation-based approach to maximum likelihood approximation applicable to general latent variable models. MCML can be described as an importance sampling method in which the likelihood ratio is approximated by Monte Carlo averages of importance ratios simulated from the complete data model corresponding to an arbitrary value of the unknown parameter. This paper studies the asymptotic (in the number of observations) performance of the MCML method in the case of latent variable models with independent observations. This is in contrast with previous works on the same topic which only considered conditional convergence to the maximum likelihood estimator, for a fixed set of observations. A first important result is that when is fixed, the MCML method can only be consistent if the number of simulations grows exponentially fast with the number of observations. If on the other hand, is obtained from a consistent sequence of estimates of the unknown parameter, then the requirements on the number of simulations are shown to be much weaker.     

Statistical and Combinatorial Aspects of Comparative Genomics*

Abstract. This document presents a survey of the statistical and combinatorial aspects of four areas of comparative genomics: gene order based measures of evolutionary distances between species, construction of phylogenetic trees, detection of horizontal transfer of genes, and detection of ancient whole genome duplications.     

关于人性论的博弈分析

中国的人性论生发出的圣人治国,是对人性的否定,产生的是囚徒困境难题;西方的人性论产生的是法律治国,是对人性的肯定,破解了囚徒困境难题.从博弈论视角看,出现如此分野的原因是,中国古代社会政治家们试图设计一种仅有帕累托最优均衡的制度,但因为没有从现实的人性出发,导致只能依靠人治维护表面的帕累托最优均衡,实际上存在的却是囚徒困境;西方社会的政治家们则以承认人性为前提,设计了一种帕累托次优均衡的制度.