A NEW(?) Probability theory proposal.
I once did a research on a special project. I’d like to share my findings and ideas with friends in this community, so I bring my proposal here. I’d be happy if my idea is of help for you.
-The start-up point of the project(Because of some reasons I set the start-up point different from the real one I did):
The research project was done for a “rescue” team to find a missed person in a forest. The rescue team would use a number of drones to find a missed person and to make the possibility of finding the target more reliable, drones would work in pairs. It is just a simple object detection. Drone A captured an object and gives the possibility of being the target-P(A), and Drone B-P(B). The problem is: If any one of P(A) and P(B) is bigger than 0.5, we don’t have to worry about missing the target. But if both of them are less than 0.5, How can we calculate the real or practical possibility of being the target?
My result is as follows:
P(T):the real(or practical)possibility of being the target
P(A):the inference possibility of being the target by Drone A
P(B):the inference possibility of being the target by Drone B
P(AM):the possibility of missing the target by Drone A
P(BM):the possibility of missing the target by Drone B
P(N):the possibility of target-non-exist
P(A)+P(N)+P(AM)=1
P(B)+P(N)+P(BM)=1
P(T)=P(A)+P(AM)*P(B)=P(A)+(1-P(A)-P(N))*P(B)=P(A)-P(A)*P(B)+(1-P(N))*P(B)=P(A)-P(A)P(B)+P(B)(P(B)+P(BM))=P(A)-P(A)*P(B)+P(B)*P(B)+P(B)*P(BM)
Here for P(B)*P(BM) part , I used RL and DL methods and for each method the result was fine enough to adopt this theory(or method) to many projects.
Conclusion:
-This method even worked well where P(A), P(B) are bigger than 0.5.
-My work tells me that this method or theory can work well for some other projects such as Autonomous vehicles, Drones, Robotics and even for LLMs.
Feel free to study or use this for your project developments or research. All work done by me and there would be no conflicts for copyrights at all.
I am open to any opinions or discussions. Thanks for your feedbacks