Sampling from arbitrary probability distribution

I need to sample lots of points from an arbitrary probability distribution but I would like to sample more points from area of high probability, like using monte carlo method for sampling illuminations for rendering purpose.

I can compute the probability (or something similar to the true probabiility) at any point in the space but I am not sure what sort algorithm I should use.

At momemt I am just sampling the parameter space uniformly, and compare the probability at the sample point with a probability sampled from a uniform distribution to decide whether the point is acceptable. Crude and quite wasteful.

I have considered importance based sampling but the various sites I visited are all about computing the value of the integral, which is not what I am interested in. Does importance sampling samples areas of high probability more or am I mistaken?

I have also looked at the Metropolis algorithm which generate a random walk that hopefully samples more from areas of high probability. This seems to be my best bet at the moment.

Any help or advice will be appreciated. I am also looking into some papers on rendering, which deals with a similar issue.

Shaobo Hou

Shaobo Hou hous1@xxxxxxxxxxxx
Just because it is not nice , doesn't mean it is not miraculous.
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