Why Does hi=p/4 Provide a Good Approximation in Spatial Scan Statistics?

[qlinsey]

I just found how to start a new topic...sorry ..

HI, dear all,

Currently I am reading the paper "spatial scan statistics: approximation and performance study " and confused with section 4.1. I read many times , but still cannot get the meaning how the formula of (4.2) come from and why hi=p /4 can give a very good approximation for the convex function? could you guide me which mathematic theoretic background I should read or...how to understand this part? Futhermore, in fact,I cannot relate lemma 4.2 to the part of explanation using Figure 3 (a),(b).

This paper --spatial scan statistics: approximation and performance study (authors: Deepal Agarwal, Andrew McGregor, etc.) , can be downloaded on website from google searching...


Hope can helpe me to figure out !

thanks !
linsey

 

[mighty2000]

Dear linsey,

Thank you for reaching out and sharing your confusion with section 4.1 of the paper "spatial scan statistics: approximation and performance study". I can understand how daunting it can be to understand complex mathematical concepts, especially when it comes to approximations and performance studies.

To answer your question about how the formula of (4.2) is derived and why hi=p/4 is a good approximation for the convex function, it is important to have a solid understanding of mathematical theories such as convex optimization and convex functions. I recommend reading up on these topics to gain a better understanding of the concepts discussed in section 4.1.

Moreover, lemma 4.2 can be related to the explanation using Figures 3 (a) and (b) by understanding the concept of convexity and how the approximations are made using a convex function. Again, a deeper understanding of convex optimization and convex functions will aid in understanding this part of the paper.

I also suggest looking at other research papers or textbooks on spatial scan statistics to gain a broader understanding of the topic. Additionally, reaching out to the authors of the paper for further clarification or seeking guidance from a mentor or colleague who has expertise in this area may also be helpful.

I hope this helps in your understanding of section 4.1. Keep persevering and seeking out resources, and I am confident you will be able to figure it out. Good luck!