……关于单变量的假设检验，包括很多免分布检验（distribution-free）。可以参考 S. Siegel 的老书《Nonparametric Statistics for the Behavioral Sciences》或者 E. Lehmann 的《Nonparametrics》。至于多维假设检验，相关资料不多，而且免分布的就更少了。为什么要是多维的？因为针对楼主例子里两个互相交互的系统，我们猜测……
…of hypothesis tests for from a single variable, including many tests that are distribution-free. See old books by S. Siegel, 'Nonparametric Statistics for the Behavioral Sciences' or E. Lehmann, 'Nonparametrics'. For multi-dimensional hypothesis tests, there's not much and still less when also distribution-free. Why multi-dimensional? Because for the two interacting systems in the example in the OP, we guess…
好吧，PG 搞了个假设检验。这方面的文献汗牛充栋，比如 E. L. Lehmann 的《Testing Statistical Hypotheses》、E. L. Lehmann 的《Nonparametrics: Statistical Methods Based on Ranks》、Sidney Siegel 的《Nonparametric Statistics for the Behavioral Sciences》。在这个场景下，PG 应该会对非参数的情况更感兴趣，也就是免分布（distribution-free）的……
Okay, PG has an hypothesis test. There's a large literature for that, e.g., E. L. Lehmann, Testing Statistical Hypotheses. E. L. Lehmann, Nonparametrics: Statistical Methods Based on Ranks. Sidney Siegel, Nonparametric Statistics for the Behavioral Sciences. In this case, PG will be more interested in the non-parametric case, i.e., distribution-free…
……（我两个都没用），等等。呃，各位，这就是统计假设检验好嘛。对不住啦。想深入了解的话，可以看看一些经典著作：E. L. Lehmann 的《Testing Statistical Hypotheses》、E. L. Lehmann 的《Nonparametrics: Statistical Methods Based on Ranks》、Sidney Siegel 的《Nonparametric Statistics for the Behavioral Sciences》。有一次我向思科展示我的工作成果，他们的反应竟然是这“不过是统计学”而已。……
…(I didn't use either), etc. Uh, it's statistical hypothesis testing, guys. Sorry 'bout that. For more, see, say some of the classics: E. L. Lehmann, Testing Statistical Hypotheses. E. L. Lehmann, Nonparametrics: Statistical Methods Based on Ranks. Sidney Siegel, Nonparametric Statistics for the Behavioral Sciences. Once I presented my work to Cisco. Their reaction was that my work was "just statistical".…
……这套数学里根本没用到“先验概率”，而蒙特卡洛（Monte Carlo）方法只是一种快速替代方案，省得去把全部 330 亿种组合都找出来。想了解更多，可以参考（附 TeX 排版标记）：E.\ L.\ Lehmann 著《{\it Nonparametrics: Statistical Methods Based on Ranks,\/}》，ISBN 0-8162-4994-6，Holden-Day 出版社，旧金山，1975 年。\ \ Jaroslav H\'ajek 与 Zbyn\v ek \v Sid\'ak 著《{\it Theory of Rank Tests,\/}》，Academia 出版社，布拉格，1967 年。\ \ Sidney……
…this math, there is no use of 'prior probabilities', and the Monte Carlo is just a fast way to replace finding all 33 billion combinations. For more, can see (with TeX markup): E.\ L.\ Lehmann, {\it Nonparametrics: Statistical Methods Based on Ranks,\/} ISBN 0-8162-4994-6, Holden-Day, San Francisco, 1975.\ \ Jaroslav H\'ajek and Zbyn\v ek \v Sid\'ak, {\it Theory of Rank Tests,\/} Academia, Prague, 1967.\ \ Sidney…
……《Techniques for Educational and Psychological Research,\/}》，John Wiley and Sons 出版社，1971 年。\ \ E.\ L.\ Lehmann 著《{\it Testing Statistical Hypotheses,\/}》，John Wiley 出版社，纽约，1959 年。\ \ E.\ L.\ Lehmann 著《{\it Nonparametrics: Statistical Methods Based on Ranks,\/}》，ISBN 0-8162-4994-6，Holden-Day 出版社，旧金山，1975 年。\ \ Jaroslav H\'ajek 与 Zbyn\v ek \v Sid\'ak 著《{\it Theory of Rank Tests,\/}》，Academia 出版社，布拉格，1967 年。\ \ Sidney……
…Techniques for Educational and Psychological Research,\/} John Wiley and Sons, 1971.\ \ E.\ L.\ Lehmann, {\it Testing Statistical Hypotheses,\/} John Wiley, New York, 1959.\ \ E.\ L.\ Lehmann, {\it Nonparametrics: Statistical Methods Based on Ranks,\/} ISBN 0-8162-4994-6, Holden-Day, San Francisco, 1975.\ \ Jaroslav H\'ajek and Zbyn\v ek \v Sid\'ak, {\it Theory of Rank Tests,\/} Academia, Prague, 1967.\ \ Sidney…
> 差距？E. L. Lehmann 著《Nonparametrics: Statistical Methods Based on Ranks》，ISBN 0-8162-4994-6，Holden-Day 出版社，旧金山，1975 年。Sidney Siegel 著《Nonparametric Statistics for the Behavioral Sciences》，McGraw-Hill 出版社，纽约，1956 年。Bradley……
> gap? E. L. Lehmann, 'Nonparametrics: Statistical Methods Based on Ranks', ISBN 0-8162-4994-6, Holden-Day, San Francisco, 1975. Sidney Siegel, 'Nonparametric Statistics for the Behavioral Sciences', McGraw-Hill, New York, 1956. Bradley…
……关于单变量的假设检验，包括很多免分布检验（distribution-free）。可以参考 S. Siegel 的老书《Nonparametric Statistics for the Behavioral Sciences》或者 E. Lehmann 的《Nonparametrics》。至于多维假设检验，相关资料不多，而且免分布的就更少了。为什么要是多维的？因为针对楼主例子里两个互相交互的系统，我们猜测……
…of hypothesis tests for from a single variable, including many tests that are distribution-free. See old books by S. Siegel, 'Nonparametric Statistics for the Behavioral Sciences' or E. Lehmann, 'Nonparametrics'. For multi-dimensional hypothesis tests, there's not much and still less when also distribution-free. Why multi-dimensional? Because for the two interacting systems in the example in the OP, we guess…
好吧，PG 搞了个假设检验。这方面的文献汗牛充栋，比如 E. L. Lehmann 的《Testing Statistical Hypotheses》、E. L. Lehmann 的《Nonparametrics: Statistical Methods Based on Ranks》、Sidney Siegel 的《Nonparametric Statistics for the Behavioral Sciences》。在这个场景下，PG 应该会对非参数的情况更感兴趣，也就是免分布（distribution-free）的……
Okay, PG has an hypothesis test. There's a large literature for that, e.g., E. L. Lehmann, Testing Statistical Hypotheses. E. L. Lehmann, Nonparametrics: Statistical Methods Based on Ranks. Sidney Siegel, Nonparametric Statistics for the Behavioral Sciences. In this case, PG will be more interested in the non-parametric case, i.e., distribution-free…
……（我两个都没用），等等。呃，各位，这就是统计假设检验好嘛。对不住啦。想深入了解的话，可以看看一些经典著作：E. L. Lehmann 的《Testing Statistical Hypotheses》、E. L. Lehmann 的《Nonparametrics: Statistical Methods Based on Ranks》、Sidney Siegel 的《Nonparametric Statistics for the Behavioral Sciences》。有一次我向思科展示我的工作成果，他们的反应竟然是这“不过是统计学”而已。……
…(I didn't use either), etc. Uh, it's statistical hypothesis testing, guys. Sorry 'bout that. For more, see, say some of the classics: E. L. Lehmann, Testing Statistical Hypotheses. E. L. Lehmann, Nonparametrics: Statistical Methods Based on Ranks. Sidney Siegel, Nonparametric Statistics for the Behavioral Sciences. Once I presented my work to Cisco. Their reaction was that my work was "just statistical".…
……这套数学里根本没用到“先验概率”，而蒙特卡洛（Monte Carlo）方法只是一种快速替代方案，省得去把全部 330 亿种组合都找出来。想了解更多，可以参考（附 TeX 排版标记）：E.\ L.\ Lehmann 著《{\it Nonparametrics: Statistical Methods Based on Ranks,\/}》，ISBN 0-8162-4994-6，Holden-Day 出版社，旧金山，1975 年。\ \ Jaroslav H\'ajek 与 Zbyn\v ek \v Sid\'ak 著《{\it Theory of Rank Tests,\/}》，Academia 出版社，布拉格，1967 年。\ \ Sidney……
…this math, there is no use of 'prior probabilities', and the Monte Carlo is just a fast way to replace finding all 33 billion combinations. For more, can see (with TeX markup): E.\ L.\ Lehmann, {\it Nonparametrics: Statistical Methods Based on Ranks,\/} ISBN 0-8162-4994-6, Holden-Day, San Francisco, 1975.\ \ Jaroslav H\'ajek and Zbyn\v ek \v Sid\'ak, {\it Theory of Rank Tests,\/} Academia, Prague, 1967.\ \ Sidney…
……《Techniques for Educational and Psychological Research,\/}》，John Wiley and Sons 出版社，1971 年。\ \ E.\ L.\ Lehmann 著《{\it Testing Statistical Hypotheses,\/}》，John Wiley 出版社，纽约，1959 年。\ \ E.\ L.\ Lehmann 著《{\it Nonparametrics: Statistical Methods Based on Ranks,\/}》，ISBN 0-8162-4994-6，Holden-Day 出版社，旧金山，1975 年。\ \ Jaroslav H\'ajek 与 Zbyn\v ek \v Sid\'ak 著《{\it Theory of Rank Tests,\/}》，Academia 出版社，布拉格，1967 年。\ \ Sidney……
…Techniques for Educational and Psychological Research,\/} John Wiley and Sons, 1971.\ \ E.\ L.\ Lehmann, {\it Testing Statistical Hypotheses,\/} John Wiley, New York, 1959.\ \ E.\ L.\ Lehmann, {\it Nonparametrics: Statistical Methods Based on Ranks,\/} ISBN 0-8162-4994-6, Holden-Day, San Francisco, 1975.\ \ Jaroslav H\'ajek and Zbyn\v ek \v Sid\'ak, {\it Theory of Rank Tests,\/} Academia, Prague, 1967.\ \ Sidney…
> 差距？E. L. Lehmann 著《Nonparametrics: Statistical Methods Based on Ranks》，ISBN 0-8162-4994-6，Holden-Day 出版社，旧金山，1975 年。Sidney Siegel 著《Nonparametric Statistics for the Behavioral Sciences》，McGraw-Hill 出版社，纽约，1956 年。Bradley……
> gap? E. L. Lehmann, 'Nonparametrics: Statistical Methods Based on Ranks', ISBN 0-8162-4994-6, Holden-Day, San Francisco, 1975. Sidney Siegel, 'Nonparametric Statistics for the Behavioral Sciences', McGraw-Hill, New York, 1956. Bradley…