Suppose that I know the stationary distribution of samplings via random walks and I want to calculate some expectation values. The stationary distribution is a discrete probability distribution. It is very costly to sample data from the stationary distribution to compute the expectations. So my question is that can I use importance sampling to compute the expectations with possible lower number of samples needed and lower variance?
From my knowledge, importance sampling can be used for continuous probability distribution. Can it be applied to discrete one?
If so, is there any available example for the discrete case?
If not, is there any sampling technique I can use to efficiently compute the expectation?
I attempted using importance sampling which requires the user to give a proposal distribution. But I find difficulties defining a discrete proposal probability distribution. Is there any guidance to achieve that for discrete case?