1. ## Bayesian Statistics Question

My current state is that I am clueless and have no idea what to do with it. Could somebody provide me some knowledge of how to start with this?

Looks tough!

3. ## Re: Bayesian Statistics Question

It's not too bad actually. But it would be nice to see some work first...

4. ## Re: Bayesian Statistics Question

Well I am trying to read up on it a bit but it's difficult..

5. ## Re: Bayesian Statistics Question

Well tell us what you do know about for this problem. For instance what do you know about getting random samples from arbitrary distributions? Do you know what a Markov Chain random sampler is or how to program one? If you had a random sample from that distribution would you know how to compute the monte carlo estimate of the integral?

6. ## Re: Bayesian Statistics Question

I have 0 knowledge at the moment, going to do some more reading. If there is anything that you can help with (hints etc), would appreciate this.

7. ## Re: Bayesian Statistics Question

It's hard to give hints when we don't know which part you're stuck on. What exactly are you trying to do at the moment?

8. ## Re: Bayesian Statistics Question

Could you tell me for example, what the easiest approach would be for this density function?

9. ## Re: Bayesian Statistics Question

What different ways do you know to obtain a sample from a distribution?

10. ## Re: Bayesian Statistics Question

Well I know how to do rejection sampling I think, but can I sample from the gamma part of it only and ignore the other part of the function?

11. ## Re: Bayesian Statistics Question

What do you mean? Use the gamma proportional to x^4*exp(-3x) as your proposed density?

12. ## Re: Bayesian Statistics Question

Yes, where alpha = 5, and beta = 3, is that plausible?

13. ## Re: Bayesian Statistics Question

As long as you make sure that the density of that gamma is always greater than the density you're trying to sample from then you're ok. You'll need to prove to yourself at least that this is the case. (But you might even want to multiply the desired density by a constant so that you aren't always rejecting your proposed point).

14. ## Re: Bayesian Statistics Question

I don't really understand, do I need to treat the other part of the density function as a uniform?

I was saying that the density of that gamma IS the density to sample from.. i.e. proposal density

15. ## Re: Bayesian Statistics Question

I would choose a density function which is always greater than the density you're trying to sample from. The term exp(-3x)*(1- exp(-2x))^7 is always smaller than 1. So, you can take g(x) = x^4. I am not sure. What do you think, Dason?