In this paper we have demonstrated the ability of the new Bayesian measure of evidence of Yin (2012, Computational Statistics, 27: 237-249) to solve both the Behrens-Fisher problem and Lindley's paradox. We have p...In this paper we have demonstrated the ability of the new Bayesian measure of evidence of Yin (2012, Computational Statistics, 27: 237-249) to solve both the Behrens-Fisher problem and Lindley's paradox. We have provided a general proof that for any prior which yields a linear combination of two independent t random variables as posterior distribution of the di erence of means, the new Bayesian measure of evidence given that prior will solve Lindleys' paradox thereby serving as a general proof for the works of Yin and Li (2014, Journal of Applied Mathematics, 2014(978691)) and Goltong?and Doguwa (2018, Open Journal of Statistics, 8: 902-914).?Using the Pareto prior as an example, we have shown by the use of?simulation results that the new Bayesian measure of evidence solves?Lindley's paradox.展开更多
文摘In this paper we have demonstrated the ability of the new Bayesian measure of evidence of Yin (2012, Computational Statistics, 27: 237-249) to solve both the Behrens-Fisher problem and Lindley's paradox. We have provided a general proof that for any prior which yields a linear combination of two independent t random variables as posterior distribution of the di erence of means, the new Bayesian measure of evidence given that prior will solve Lindleys' paradox thereby serving as a general proof for the works of Yin and Li (2014, Journal of Applied Mathematics, 2014(978691)) and Goltong?and Doguwa (2018, Open Journal of Statistics, 8: 902-914).?Using the Pareto prior as an example, we have shown by the use of?simulation results that the new Bayesian measure of evidence solves?Lindley's paradox.
文摘现有贝叶斯压缩感知(Bayesian Compressed Sensing,BCS)-逆合成孔径雷达(Inverse Synthetic Aperture Radar,ISAR)成像算法中先验分布模型不能很好地满足可压缩性,导致成像精度随脉冲数目的减小、高斯噪声的增强而急剧下降。为此,提出了一种基于广义Pareto分布改进BCS成像方法(Improving BCS imaging based on GPD,IGPCS)。该方法主要在BCS框架下利用广义Pareto先验分布替代传统的广义Gaussian先验分布,以增强模拟信号的稀疏先验和可压缩性。进一步地,为了克服后验概率模型计算困难等问题,采用最大后验(Maximum A Posteriori,MAP)方法对超参数进行估计。通过对Mig-25小型飞机的ISAR模拟实验表明,与传统方法相比,IGPCS方法能够获取极高的成像精度,并且对低脉冲数、强高斯噪声环境具有较强的鲁棒性。
