SOA Problem #5

[BAIINinja]

I am having a hard time with the bayesian problems, looking at the solution I do not understand what it is doing. Does anyone have any better way of explaining the bayesian process?

[Celtics4Life]

can you be specific on which part of the solution is confusing? is it the first step of how they arrived at q^5(1-q)^2 as the expression to integrate?

[BAIINinja]

yes, the first line I am not understanding

[truonda]

I think the first proportional to symbol should actually be an equal sign. Does that make things clearer?

[Celtics4Life]

the main thing about bayesian is finding a posterior distribution for q given the data you have observed:

pr(q|data) = [ pr(data|q)*pr(q) ] / pr(data)

This similar to the conditional probability formula.

pr(data|q) is just probability of seeing 1 claim twice which is going to be

2q(1-q) * 2q(1-q)

pr(q) is given as 4q^3

pr(data) can be ignored and just called a constant C since it is going to evaluate to some number.

from this step you can tell that the distribution is some constant C*q^5(1-q)^2. next compare this to your table of distributions and figure out what C is supposed to be.

[BAIINinja]

ok, so is the reason the ceofficients are taken away due to them getting cancelled out in the posterior formula?

[Celtics4Life]

the constants didnt get cancelled out - you figure out the constant in two ways
1) integrate the expression Cq^5(1-q)^2 from 0 to 1 and set it equal to 1 and then solve for C
2) recognize that this is a known distribution and deduce C from the formula for the pdf of that known distribution.

[BAIINinja]

Ok I see, thank you for th help.