An algorithm of continuous stage space MCMC method for solving algebra equation f(x) =0 is given.It is available for the case that the sign of f(x) changes frequently or the derivative f′(x) does not exist in th...An algorithm of continuous stage space MCMC method for solving algebra equation f(x) =0 is given.It is available for the case that the sign of f(x) changes frequently or the derivative f′(x) does not exist in the neighborhood o f the root,while the Newton method is hard to work.Let n be the number of random variables created by computer in our algorithm.Then after m=O(n) transactions from the initial value x 0,x * can be got such that |f(x *)|<e -cm |f(x 0)| by choosing suitable positive constant c. An illustration is also given with the discussion of convergence by adjusting the parameters in the algorithm.展开更多
Bayes统计学能够从空中楼阁的理论广泛地落地于自然科学、经济学和社会学等领域,得益于计算机技术和马尔可夫链蒙特卡洛(Markov chain Monte Carlo,简称MCMC)法的发展。文章介绍了MCMC方法在Bayes推断中的应用,主要讨论了MCMC方法中的...Bayes统计学能够从空中楼阁的理论广泛地落地于自然科学、经济学和社会学等领域,得益于计算机技术和马尔可夫链蒙特卡洛(Markov chain Monte Carlo,简称MCMC)法的发展。文章介绍了MCMC方法在Bayes推断中的应用,主要讨论了MCMC方法中的独立抽样和随机游走抽样的Metropolis-Hastings(M-H)算法,利用可读性较强的Matlab程序来实现两种抽样算法,并给出了详细的程序实施过程,分析了两种抽样的优缺点。模拟分析结果表明:独立抽样M-H算法比较容易实施,但是要求建议分布和后验分布的吻合度较高,否则计算效率低下,而且模拟效果不理想;随机游走抽样的M-H算法不需要建议分布接近后验分布,模拟效果也比较好,因此,克服了独立抽样算法的不足,适用范围更广。展开更多
基金Supported by the National Natural Science Foundation of China(70 1 71 0 0 8)
文摘An algorithm of continuous stage space MCMC method for solving algebra equation f(x) =0 is given.It is available for the case that the sign of f(x) changes frequently or the derivative f′(x) does not exist in the neighborhood o f the root,while the Newton method is hard to work.Let n be the number of random variables created by computer in our algorithm.Then after m=O(n) transactions from the initial value x 0,x * can be got such that |f(x *)|<e -cm |f(x 0)| by choosing suitable positive constant c. An illustration is also given with the discussion of convergence by adjusting the parameters in the algorithm.
文摘Bayes统计学能够从空中楼阁的理论广泛地落地于自然科学、经济学和社会学等领域,得益于计算机技术和马尔可夫链蒙特卡洛(Markov chain Monte Carlo,简称MCMC)法的发展。文章介绍了MCMC方法在Bayes推断中的应用,主要讨论了MCMC方法中的独立抽样和随机游走抽样的Metropolis-Hastings(M-H)算法,利用可读性较强的Matlab程序来实现两种抽样算法,并给出了详细的程序实施过程,分析了两种抽样的优缺点。模拟分析结果表明:独立抽样M-H算法比较容易实施,但是要求建议分布和后验分布的吻合度较高,否则计算效率低下,而且模拟效果不理想;随机游走抽样的M-H算法不需要建议分布接近后验分布,模拟效果也比较好,因此,克服了独立抽样算法的不足,适用范围更广。
