I implemented a Pi estimation program in C, that is I generate a pair of PRNs using LCG algorithm, and then I compute their coordinates to see if they fall within a unit disk, as referenced here https://www.geeksforgeeks.org/estimating-value-pi-using-monte-carlo/.
Now since this application is quite trivial, I also already implemented a program that estimates euler’s number using similar method, as referenced in this paper: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9170329
What bothers me is the following:
The Pi estimation and e estimation examples demonstrate what Monte Carlo Methods can do, specifically Accept/reject method. This method can be generically apply to estimate many definite integrals, but I do not just present a random integral that have numbers do not mean anything.
As I am working on a demo, I would like to find a more interesting integral, that may be useful such that I can demonstrate a real-world (straightforward) usage of Monte Carlo Accept/Reject method. Is there a specific example that does so?
I found a paper that estimates the volume of a bell: Montecarlo Methods to Efficently Compute Volume of Solids, which seems very interesting, but they are not using accept/reject method here. I looked at many other Monte Carlo papers, but I found it difficult to implement the integrals from papers as theory behind is too complicated.
I understand the example that I am looking for may not be trivial to find, but any pointers would be great!
Thanks