# Thread: Question on Bayesian Learning and Probability Theory

1. ## Question on Bayesian Learning and Probability Theory

I have some difficulties at solving a traditional problem where we have two hats, hat A and B, where there are black and white balls in each hats but the experimenter does not know the proportion of $\displaystyle$a$$black balls in hat A and proportion \displaystyle b$$ for hat B. Let $\displaystyle$0 \le a, b \le 1$$with \displaystyle a \ne b$$. The proportion of hat A is $\displaystyle$p_0 \in (0,1)$$. The experimenter draws randomly some balls (with replacement) to determine which of the hats he is drawing from. After each \displaystyle k$$ draws, the experimenter updates his beliefs using Bayes' rule. Denote $\displaystyle$p_k$$where \displaystyle k=1,2,...,$$ the experimenter posterior probability after k balls have been drawn.

My questions are:

4. ## Re: Question on Bayesian Learning and Probability Theory

Thanks for the help chiro. yes that's what I was thinking... but can $\displaystyle$p_k be stochastic?

5. ## Re: Question on Bayesian Learning and Probability Theory

Absolutely: It can have a distribution and the point with this problem is that it really has to since you don't know the distribution (in terms of balls) and hence don't know the ratio.

This is a great example of using the Bayesian method for a problem that is well suited (in terms of what information you know and the models you can use).