- #1
slipperypete
- 3
- 0
Let X be the set X=\left\{x_1,x_2,...,x_n\right\}, where each x_i is a Bernoulli random variable and P be the set P=\left\{p_1,p_2,...,p_n\right\}, where p_i is the probability that x_i=1. Now, suppose there are two other sets, A=\left\{a_1,a_2,...,a_n\right\} and B=\left\{b_1,b_2,...,b_n\right\}, where a_i,b_i are two different estimates for p_i.
In other words, p is the "true" (unknown) probability that x will occur, and a and b are both attempts to estimate that probability.
I am trying to design an experiment that will determine which set, A or B, is "closer" to P.
If these Bernoulli random variables represented, say, different-sided dice, then an experiment would be pretty straightforward: conduct a Bernoulli process; i.e., repeatedly perform a Bernoulli trial.
However, in my case, each x_i represents a real-world event, and can be simulated only once. A Bernoulli process is impossible, I am limited to a single Bernoulli trial. If X=\left\{x_1,x_2,x_3\right\}, then I don't think there would be a practical way to solve this problem at any level of significance. But n here is actually quite large, so I feel like there should be some test which would allow me to show A>B or A<B or A\neq B or A=B.
Any thoughts?
In other words, p is the "true" (unknown) probability that x will occur, and a and b are both attempts to estimate that probability.
I am trying to design an experiment that will determine which set, A or B, is "closer" to P.
If these Bernoulli random variables represented, say, different-sided dice, then an experiment would be pretty straightforward: conduct a Bernoulli process; i.e., repeatedly perform a Bernoulli trial.
However, in my case, each x_i represents a real-world event, and can be simulated only once. A Bernoulli process is impossible, I am limited to a single Bernoulli trial. If X=\left\{x_1,x_2,x_3\right\}, then I don't think there would be a practical way to solve this problem at any level of significance. But n here is actually quite large, so I feel like there should be some test which would allow me to show A>B or A<B or A\neq B or A=B.
Any thoughts?