I have run 1,000,000 experiments. Each experiment consists of 5 trials with binary outcomes, either L (for left) or R (for right).
However, I’m not going to tell you how I’ve picked my experiments. Maybe I’m just flipping a fair coin each time. Maybe I’m using a biased coin. Or maybe I’m doing something completely different, like dropping a bouncy ball down a mountain and checking whether it hits a red rock or a white rock first—and different experiments are conducted on different mountains. I might be doing some combination of all three.
You do get one guarantee, though: All the experiments are Bernoulli processes. In particular, the order of the trials is irrelevant.
Your goal is to guess the marginal frequencies of the fifth trial. For each k=0,1,…,4, you need to tell me the frequency that the fifth trial is an R given that k of the outcomes of the first four trials are R.
For example, if every experiment is just flipping a fair coin, then the fifth trial will be an R with probability 1/2, no matter what the first four are. However, if I’m using biased coins, then the frequency of R will increase the more Rs seen.
To help you in your guessing, I have provided a csv of all the public trials. As an answer, please provide a list like [0.3, 0.4, 0.5, 0.6, 0.7] of your frequencies—the kth element of your list is the marginal frequency over the experiments with k of the first four trials being R.
I haven’t yet looked at the frequencies myself, but I will do so shortly after posting this. If you want to test your guesses against others, I have created a market on Manifold Markets. I will resolve the market before I reveal the correct frequencies, which will happen in around two weeks, but maybe earlier or later depending on trading volume.
Experiment: Test your priors on Bernoulli processes.
I have run 1,000,000 experiments. Each experiment consists of 5 trials with binary outcomes, either L (for left) or R (for right).
However, I’m not going to tell you how I’ve picked my experiments. Maybe I’m just flipping a fair coin each time. Maybe I’m using a biased coin. Or maybe I’m doing something completely different, like dropping a bouncy ball down a mountain and checking whether it hits a red rock or a white rock first—and different experiments are conducted on different mountains. I might be doing some combination of all three.
You do get one guarantee, though: All the experiments are Bernoulli processes. In particular, the order of the trials is irrelevant.
Your goal is to guess the marginal frequencies of the fifth trial. For each k=0,1,…,4, you need to tell me the frequency that the fifth trial is an R given that k of the outcomes of the first four trials are R.
For example, if every experiment is just flipping a fair coin, then the fifth trial will be an R with probability 1/2, no matter what the first four are. However, if I’m using biased coins, then the frequency of R will increase the more Rs seen.
To help you in your guessing, I have provided a csv of all the public trials. As an answer, please provide a list like [0.3, 0.4, 0.5, 0.6, 0.7] of your frequencies—the kth element of your list is the marginal frequency over the experiments with k of the first four trials being R.
I haven’t yet looked at the frequencies myself, but I will do so shortly after posting this. If you want to test your guesses against others, I have created a market on Manifold Markets. I will resolve the market before I reveal the correct frequencies, which will happen in around two weeks, but maybe earlier or later depending on trading volume.
Good luck!