I have a function 'P(x)' where we query for any 'x' it gives a probability value. This function 'P' does not have a closed form and the evaluation is costly. Now 'x' is a set of vectors(matrix whose rows) which sum to 1 and each entry in the matrix is greater that 0.Now this distribution has many peaks and ridges. What method would be appropriate to sample from this 'P'. I want to approximate the distribution by a set of samples. So what would be the appropriate method to use? Which method in MCMC or any would be suitable?
What algorithm should I use for sampling from a black box probability function?
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