Drawing samples from a target distribution is essential for statistical computations when the analytical solution is infeasible. Many existing sampling methods may be easy to fall into the local mode or strongly depend on the proposal distribution when the target distribution is complicated. In this article, the Global Likelihood Sampler (GLS) is proposed to tackle these problems and the GL bootstrap is used to assess the Monte Carlo error. GLS takes the advantage of the randomly shifted low-discrepancy point set to sufficiently explore the structure of the target distribution. It is efficient for multimodal and high-dimensional distributions and easy to implement. It is shown that the empirical cumulative distribution function of the samples uniformly converges to the target distribution under some conditions. The convergence for the approximate sampling distribution of the sample mean based on the GL bootstrap is also obtained. Moreover, numerical experiments and a real application are conducted to show the effectiveness, robustness, and speediness of GLS compared with some common methods. It illustrates that GLS can be a competitive alternative to existing sampling methods.

周永道，南开大学统计与数据科学学院教授、博导，入选国家、天津市以及南开大学等多个人才项目。研究方向为试验设计和数据挖掘。主持过5项国家自然科学基金、1项天津市自然科学基金重点项目及其它10余项纵横向项目。曾访问UCLA、曼彻斯特大学等5所境外高校。在统计学顶级期刊JRSSB, JASA、Biometrika及中国科学等国内外期刊发表学术论文50余篇；在Springer等出版社合作出版了3部中英文专著和2部统计学专业教材。曾获国家统计局统计科学研究优秀成果奖一等奖。现为中国数学会均匀设计分会秘书长、泛华统计协会永久会员、美国《数学评论》评论员。