军事欺骗战法分析的数学方法-应用

针对军事欺骗战法定量分析困难的问题,采用基于贝叶斯统计推断和博弈均衡分析的数学方法,在理论上为解决此难题提供了一种可行的方法。该方法首先定义基本概率矩阵,然后根据贝叶斯原理为交战双方构造用于统计推断的主观概率矩阵,并在由两个主观概率矩阵元素构成的偏序链与实施军事欺骗机会之间建立对应关系,再将此关系推广到基本概率矩阵,即是否存在实施军事欺骗的机会将由基本概率矩阵元素构成的偏序链决定。对理论成果的初步应用表明：通过分析由战场情报信息构成的基本概率矩阵的偏序链,可以科学地运用军事欺骗和反军事欺骗战法。     

改进的累量域波达方向矩阵法

构造了一种可以进行高分辨二维波达方向估计的累量域波达方向矩阵。利用该矩阵的特征值和特征向量 ,就可以求出信号源的方位角和俯仰角。同其它的波达方向矩阵法相比 ,放宽了对阵列结构的要求 ,提高了阵列孔径的利用率。同时 ,由于采用了累量来构造波达方向矩阵 ,因此新方法具有对高斯噪声的自然盲性。     

考虑验前信息可信度时的Bayes估计

研究了考虑验前信息可信度时的验前分布和Bayes估计算法,给出了正态总体参数的Bayes估计方法。以导弹落点散布的估计为例,说明了考虑验前信息可信度时Bayes估计有明显的改善,即具有更好的可信度。     

一种新的非线性/非高斯滤波方法

自主滤波方法是一种递归式贝叶斯估计方法 ,该方法采用一组抽样值来近似目标状态的概率密度函数 ,可用于非线性系统模型和观测模型、非高斯观测噪声条件下的滤波。将该算法与扩展卡尔曼滤波方法进行了比较 ,仿真结果表明 ,该算法性能优于扩展卡尔曼滤波方法     

再入飞行器落点准确度的统计分析

本文研究再入飞行器的落点准确度(系统性偏差)的检验和估计方法。首先,文中引入了准确度的容许限的概念,在此基础上给出了Bayes验后加权概率比检验方法。关于落点系统偏差的估计,讨论了Bayes估计方法及带有约束的Bayes估计方法。文中注意了充分运用试验前的信息,以便使落点系统偏差的评估能在小子样场合下进行。     

基于贝叶斯混合源分离方法的声纳探测误差模型

声纳的探测误差模型是声纳仿真的核心技术。针对现有的声纳误差白噪声模型仿真逼真度低的问题,提出了基于贝叶斯混合源分离方法,建立了声纳的探测误差模型,提高了声纳误差模型的性能。与传统的白噪声仿真方法相比,基于贝叶斯混合源分离方法的声纳误差仿真模型具有较好的逼真度,可以有效地对声纳探测误差进行建模和预测。     

Bayesian selling problem with partial information

We introduce an optimal stopping problem for selling an asset when the fixed but unknown distribution of successive offers is from one of n possible distributions. The initial probabilities as to which is the true distribution are given and updated in a Bayesian manner as the successive offers are observed. After receiving an offer, the seller has to decide whether to accept the offer or continue to observe the next offer. Each time an offer is observed a fixed cost is incurred. We consider both the cases where recalling a past offer is allowed and where it is not allowed. For each case, a dynamic programming model and some heuristic policies are presented. Using simulation, the performances of the heuristic methods are evaluated and upper bounds on the optimal expected return are obtained. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Bayesian sampling plans for exponential distributions with interval censored samples

This article studies the problem of designing Bayesian sampling plans (BSP) with interval censored samples. First, an algorithm for deriving the conventional BSP is proposed. The BSP is shown to possess some monotonicity. Based on the BSP and using the property of monotonicity, a new sampling plan modified by the curtailment procedure is proposed. The resulting curtailed Bayesian sampling plan (CBSP) can reduce the duration time of life test experiment, and it is optimal in the sense that its associated Bayes risk is smaller than the Bayes risk of the BSP if the cost of the duration time of life test experiment is considered. A numerical example to compute the Bayes risks of BSP and CBSP and related quantities is given. Also, a Monte Carlo simulation study is performed to illustrate the performance of the CBSP compared with the BSP. The simulation results demonstrate that our proposed CBSP has better performance because it has smaller risk. The CBSP is recommended. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 604–616, 2015     

Sequential learning versus no learning in Bayesian regression models

We consider two regression models: linear and logistic. The dependent variable is observed periodically and in each period a Bayesian formulation is used to generate updated forecasts of the dependent variable as new data is observed. One would expect that including new data in the Bayesian updates results in improved forecasts over not including the new data. Our findings indicate that this is not always true. We show there exists a subset of the independent variable space that we call the “region of no learning.” If the independent variable values for a given period in the future are in this region, then the forecast does not change with any new data. Moreover, if the independent variable values are in a neighborhood of the region of no learning, then there may be little benefit to wait for the new data and update the forecast. We propose a statistical approach to characterize this neighborhood which we call the “region of little learning.” Our results provide insights into the trade‐offs that exist in situations when the decision maker has an incentive to make an early decision based on an early forecast versus waiting to make a later decision based on an updated forecast. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 532–548, 2014     

Asymmetric information and third-party intervention in civil wars

I study a two-period model of conflict with two combatants and a third party who is an ally of one of the combatants. The third party is fully informed about the type of her ally but not about the type of her ally’s enemy. In a signaling game, I find that if the third party is unable to give a sufficiently high assistance to her ally, then there exists a unique separating equilibrium in which the third party’s expected intervention causes her ally’s enemy to exert more effort than in the absence of third-party intervention; this worsens the conflict.