# Thread: Is there a difference between posterior denisty and posterior distribution?

1. ## Is there a difference between posterior denisty and posterior distribution?

Is there a difference between posterior denisty and posterior distribution? Or are they 2 names for the same thing?

2. Posterior Density refers to the pdf of the posterior distribtuion.

3. ok so does that mean that if iv got a posterior distribution of $x^{101}$ $e^{-29x/2}$, thats fine is it? so if i need it to be a pdf do i need to change it? because if i integrate it over 0....infinity it doesnt sum to 1?

Is this where i would need a multiplier "k" in the posterior density?

4. can you write down your question or show how you got till there? What you have mentioned as your posterior distribution looks to me like the kernel of a gamma distribution.

5. Suppose that a random sample of size n = 100 from an exponential distribution with parameter is about to be collected. It is thought that a Ga(2, 2) prior distribution for is appropriate but, since it is believed that values of exceeding 6 are impossible, the prior distribution is truncated above 6.

Calculate the prior probability that exceeds 6 assuming the truncated prior distribution. What is the probability when the prior distribution is not truncated?

Suppose the data yield ¯x = 1/8. Calculate the posterior probability that
exceeds 6 assuming the truncated prior distribution. What is the probability
when the prior distribution is not truncated?

6. so i integrated my prior function over the range 0....6 and set it equal to 1 to find my constant "k" to make it a valid distribution.

i found "k" to be 4/(1-13exp{-12})

then from here i started getting confused as to how to calculate the prior probabilities. I guess thats when i started getting mixed up between densities and distributions?

Would you be able to walk me through what you did, I have attained answers but really not sure whether iv used the correct integrals or not because of my confusion! :-s

7. The probability distribution is the function that maps sets to probabilities. The density is the function that you integrate over. So, for example a distribution would be a function $\phi$ such that $\phi(A) = P(X \in A)$ whereas the density is the function $f$ such that $\int_A f(x) \ dx = P(X \in A)$.

If the question asks to find the posterior distribution, reporting the density should be enough to satisfy whoever is asking the question.