I am again posting the hypothesis problem
In table I, xi is the i
th observations received from the neighbor vehicles about the event E1. The event E1 represents the occurrence of an event and E1' represents non-occurrence of the event E1 There are different methods to determine the occurrence of the event E1. We use Threshold Random Walk (TRW) technique to calculate the decision about the occurrence about the event. The TRW makes the detection as quickly as possible with high probability of being correct.
Here, Xi=x1,x2,x3..., be the observation about the event from neighbor vehicles. We assume that Xi is independent and identically distribute (i.i.d.) and that the observations are independent across each vehicle For a given event, let Xi be a random variable (indicator) that represents truth-telling probability of event E1.To make the procedure simple,suppose the random variable Xi can take only two values 0 and 1, where
(But my teacher said this is not the correct way to represent Xi, here theta is the truth-telling probability in my case)
so can I represent Xi as this:=>
So by using sequential analysis we can make the decision as we observe the outcomes.
Lets consider two hypotheses, one is null and other is alternate hypothesis viz. H0 andH1, where H0 is the hypothesis that event E1has occurred and H1 is the hypotheses that event E1has not occured (i.e. E1'). We also assume that the conditional on the hypotheses, X|Hj, j= 0,1 are i.i.d and there are four possible outcomes when a decision is made.
I want to represent something like this:=>
Where Pr[X|Hj] is the the conditional probability of the trust observation X given the hypotheses Hj is true and X is the truth-telling probability observed so far. If the algorithm chooses H0 instead of H1 then the error probability is a false negative (i.e. type 1 error probability) and if algorithm chooses H1 instead of H0 when infact H0 is true, then the error probability is false positive (i.e. type 2 error probability).
Here, I have a problem in representing Xi={ 0 and 1 ..... }
and I would like to know how can I find the values of Pr [Xi|H0] and Pr [Xi|H1]
I have moved your posting from the first forum you saw ("News") to a topic-appropriate category ("Statistics").
However, I cannot fix the links to files on your own computer, as displayed in the table above.
I'm sorry, but nobody (with any Internet savvy) is going to open a ZIP file from an unknown source.
Please reply here with the actual images (not links to your hard drive), the full and exact text of the exercise on which you're working, the complete instructions, and a clear statement of your thoughts and efforts so far. Thank you.
