This article addresses the issue of computing the constant required to implement a specific nonparametric subset selection procedure based on ranks of data arising in a statistical randomized block experimental design...This article addresses the issue of computing the constant required to implement a specific nonparametric subset selection procedure based on ranks of data arising in a statistical randomized block experimental design. A model of three populations and two blocks is used to compute the probability distribution of the relevant statistic, the maximum of the population rank sums minus the rank sum of the “best” population. Calculations are done for populations following a normal distribution, and for populations following a bi-uniform distribution. The least favorable configuration in these cases is shown to arise when all three populations follow identical distributions. The bi-uniform distribution leads to an asymptotic counterexample to the conjecture that the least favorable configuration, i.e., that configuration minimizing the probability of a correct selection, occurs when all populations are identically distributed. These results are consistent with other large-scale simulation studies. All relevant computational R-codes are provided in appendices.展开更多
使用反例压缩算法,从反例中剔除冗余信息,从而使反例易于理解,是目前的研究热点.然而,目前压缩率最高的BFL（brute force lifting）算法,其时间开销过大.为此,提出一种基于悖论分析和增量式SAT（boolean satisfiablilty problem）的快...使用反例压缩算法,从反例中剔除冗余信息,从而使反例易于理解,是目前的研究热点.然而,目前压缩率最高的BFL（brute force lifting）算法,其时间开销过大.为此,提出一种基于悖论分析和增量式SAT（boolean satisfiablilty problem）的快速反例压缩算法.首先,根据反证法和排中律原理,该算法对每一个自由变量v,构造一个SAT问题,以测试v是否能够避免反例.而后对其中不可满足的SAT问题,进行悖论分析,抽取出导致悖论的变量集合.所有不属于该集合的变量,均可作为无关变量直接剔除.同时,该算法使用增量式SAT求解方法,以避免反复搜索冗余状态空间.理论分析和实验结果表明,与BFL算法相比,该算法能够在不损失压缩率的前提下获得1～2个数量级的加速.展开更多
文摘This article addresses the issue of computing the constant required to implement a specific nonparametric subset selection procedure based on ranks of data arising in a statistical randomized block experimental design. A model of three populations and two blocks is used to compute the probability distribution of the relevant statistic, the maximum of the population rank sums minus the rank sum of the “best” population. Calculations are done for populations following a normal distribution, and for populations following a bi-uniform distribution. The least favorable configuration in these cases is shown to arise when all three populations follow identical distributions. The bi-uniform distribution leads to an asymptotic counterexample to the conjecture that the least favorable configuration, i.e., that configuration minimizing the probability of a correct selection, occurs when all populations are identically distributed. These results are consistent with other large-scale simulation studies. All relevant computational R-codes are provided in appendices.
文摘使用反例压缩算法,从反例中剔除冗余信息,从而使反例易于理解,是目前的研究热点.然而,目前压缩率最高的BFL（brute force lifting）算法,其时间开销过大.为此,提出一种基于悖论分析和增量式SAT（boolean satisfiablilty problem）的快速反例压缩算法.首先,根据反证法和排中律原理,该算法对每一个自由变量v,构造一个SAT问题,以测试v是否能够避免反例.而后对其中不可满足的SAT问题,进行悖论分析,抽取出导致悖论的变量集合.所有不属于该集合的变量,均可作为无关变量直接剔除.同时,该算法使用增量式SAT求解方法,以避免反复搜索冗余状态空间.理论分析和实验结果表明,与BFL算法相比,该算法能够在不损失压缩率的前提下获得1～2个数量级的加速.
