Statistical inference and Monte Carlo algorithms

Summary This review article looks at a small part of the picture of the interrelationship between statistical theory and computational algorithms, especially the Gibbs sampler and the Accept-Reject algorithm. We pay particular attention to how the methodologies affect and complement each other. Read before the Spanish Statistical Society at a meeting organized by the University of Granada on Friday, September 27, 1996     

Rao-Blackwellized粒子势均衡多目标多伯努利滤波器

由于多伯努利滤波器直接近似递推了多目标状态的后验概率密度,使得多目标跟踪问题在基于随机有限集理论框架下的求解及目标状态的估计显得更为直观.本文针对一个状态可分解(线性/非线性)的状态空间模型,分析基于Rao-Blackwell定理的滤波估计方法,结合噪声的去相关构造线性状态的滤波方程.文中详细推导并提出Rao-Blackwellized粒子势均衡多目标多伯努利滤波器的一般实现形式,包括给出多伯努利非线性状态粒子滤波的实现形式,并结合非线性滤波结果给出多伯努利线性状态的递推滤波公式.本文提出的滤波器实现方法能够在更低维的状态空间上进行采样,滤波器的整体跟踪性能得到提高.多目标跟踪的仿真实验结果验证了该算法的有效性.     

基于分层空间的Rao-Blackwellised化粒子滤波算法

针对于粒子滤波在目标跟踪里面粒子使用率低且单一等问题,提出一种基于分层空间的Rao-Blackwellised化粒子滤波算法。该算法通过Rao-Blackwell定理将线性变量边缘化从而减少状态空间维数,提高估计精度。在满足同等精度要求时,可大大减少所需粒子数目,因而大大降低计算负荷;分层理论可以把粒子空间分成多重空间,利用权重实现合理分配粒子,可以提高相关估计的准确性。实验结果表明,所提算法的均方根误差相比传统算法降低了50%,精确度在每个仿真时间内都有提高。     

A Note on the Estimation of Pr {Y < X} in the Exponential Case

The minimum variance unbiased estimation of Pr (Y < X) under the assumption that X and Y are independently negative exponentially distributed is derived in closed form. Results assume simpler forms than those in the normal case obtained by Church and Harris (1970) and Downton (1973).