帮我看看英语,高维积分的数值计算的

orionsnow

基础语法错误已经纠正过了，主要担心数学问题， 怕我的问题和意思没有表达清楚。

文章的内容是关于高维积分的数值计算的，问题主要是关于时间，准确度和稳定性的。

General Comments: The idea of this paper is good; it provides us a new algorithm to calculate the multivariate normal distribution with higher computation speed and better digits of precision than the older.  The order of the computation time is up to “(P-1)!” for current analytical algorithm.  The order of theQuasi monte-carlo is approximately linear, but the digit is limited to five.
However, there are a few things and questions that the author might need to improve and answer in the future.

#1, It would be better if the author can briefly cut some part, which is  too detailed.  
1.1 S2.4 (p 9 line 47),
This section could be reduced. There are too many details, which is overlapped with the theory section 2.1 2.2 and 2.3 .
1.2 S4( improving numerical conditions),  
This section could be reduced too, If the skills you used is not totally new (refer to Miwa)

#2
For computational time and digit.
2.1  p3 line 15:  “ more slowly than for existing method”, which  method are you comparing with? (Miwa or Craig?), how much is its order exactly?   ( e.g  (p-1)! for miwa,   <=  (p-1)! For Craig). Also refer to the general comments
2.2 Table 1 and Table 2 :   maybe the author could add the comparison with Miwa or Craig,  including the computational time and under which environment this computation is carried (Which language is the program used? C, Fortran or R?),  ,  refer to Craig 2008,  Mi et. al. 2010, Phinikettos and Gandy 2011
2.3 Is the program open-source or available to download for special (academic) purpose?   
2.4 For Table 2:  why set \rho = 0, is a dummy test valuable to be published?  
Btw, it would be very interesting for the reader to see a dependent examples ( e.g. \rho=0.5) with  coordinates that have different signs  (e.g  (-a, -a, -a, 6a) ), which is practical in several conditions.
2.5 Have the author tried very small value of u? (e.g  u<0.0001), under this condition some methods need to redesign the allocation of grids (the default interval is too large).   However the methods that use qasi monte carlo  algrithm do not have such problem

#3
Some typos and else.
3.1 Equation 3 in p4
I would guess there is a “=” or “+” missing in the second and third line of the equation 3.  Am I right?
3.2 P6 line 10
Why was it called longitudinal inequality? I was confused here.  After reading several paragraphs later, I realized that this is named after an order sequence. Maybe one or two sentence could be written to cover the gap.

Comments to the Editors
Dear Editors,
Thank you very much for giving me this paper to review.  I am happy to be updated with the news from multivariate normal integral and learn new algorithms.
It is a quite interesting paper, which provides new thinking to calculate multivariate integral with a faster speed.
Here are some minor points that I would like to say:
The paper is little bit redundant. There are also some part is not detailed enough and some further comparison that need to be carried out.
My Recommendation is Minor Revision and I would like to read it again.
Best Regards

aileute

这段话里有大量语法错误和不精确措辞。这是你的review，也不需要语言上完全没有语法错误。但是请注意专业用语，general comments里我大概可以推测你想要说的问题runtime complexity，但是专业术语没有出来，我也不敢确定你到底是不是指这个问题。

orionsnow

好的，谢谢。 关键是能不能让人看明白，我怕我写了人家看不明白，就白写了。 各种语法错误都欢迎指出。

你是要说 算法复杂度分析吧 ？ Computational complexity ？

我在这个领域的杂志里头没有见过这个词，不知道能不能用。

原文是，  the computational time is proportional to p^2 * 2 ^ (p-1), for p dimensional problem.

日本教授miwa 那篇文章也是用的 computational time。  

“However,
one major difficulty of the Monte Carlo method is that the computational time increases by
about 100 times to achieve an increase of one decimal place in the accuracy.
”

不过这两个人都是日本人，我回头去查查母语者的文献去。 也可能和应用计算统计学更关心具体时间消耗有关系， 理论算法复杂度一般不作深入讨论。

说到这里，我发现自己一个语法错误。 是computational time 不是 computation time 。