I am not sure this helps, but ...
if you don't know of the rgamma function in R, type in ?rgamma into the console.
Dear Ebert,
The PDF is as f(x,y,z)=cons.g0(x)g1(y|x)g2(z|x), where g0(x) is not gamma. We should find a method to generate sample of g0(x).
Hi Kambiz,
At the risk of stating the obvious, the general method for generating random variates from an arbitrary probability distribution function is called inverse transform sampling.
http://en.wikipedia.org/wiki/Inverse_transform_sampling
This does require knowing the cumulative probability distribution, which looks nontrivial in your case. Will a numerical approximation be good enough?
Best of luck,
I was, perhaps mistakenly, thinking that you would not have to generate the PDF of g0(x) directly. You provide a formula for g0(x). The numerator contains xa. If you know that x is distributed normally with mean 7 and variance of 12, and you know that a is distributed runif(min=4, max=7) raised to a rnorm(mean=3, sd=18) exponent. I have no idea what the PDF of xa is, but now I can get R to sample this distribution. I can either take numbers directly from this function, or I can generate a population of 5,000,000 values and then randomly sample from this population. Just do this for all the other parts of go(x). I realize that this does not directly answer your question, but sometimes an indirect approach can be just as useful.
Dear Tran,
Thanks for your answer. Since I am not familiar with Slice sampling, please explain about this method based on g_0(x) in my question.
Since y|x,z or z|x,y are all easily simulated from. Probably you only need to sample from x|y,z using any appropriate MCMC sampler that you are familiar with. I recommend looking at Slice sampling, Neal 2003.
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Techniques
- Meta-Analysis