If the target distribution is not uniform, can we use stratified sampling?
keenan
@zhengbol Yes, and it will reduce variance (or rather, ensure that variance does not increase) for the same reason that it works for a uniform distribution: the integrand is partitioned into regions, each of which have variance no greater than the whole integrand.
However, it may indeed be true that uniform bins are no longer optimal in the sense that they do not provide the greatest possible reduction in variance.
If you know, ahead of time, that you are going to "warp" your uniform samples (as in the case of, say, cosine-weighted importance sampling), how might you choose bins differently in order to reduce variance? What's the guiding principle?
If the target distribution is not uniform, can we use stratified sampling?
@zhengbol Yes, and it will reduce variance (or rather, ensure that variance does not increase) for the same reason that it works for a uniform distribution: the integrand is partitioned into regions, each of which have variance no greater than the whole integrand.
However, it may indeed be true that uniform bins are no longer optimal in the sense that they do not provide the greatest possible reduction in variance.
If you know, ahead of time, that you are going to "warp" your uniform samples (as in the case of, say, cosine-weighted importance sampling), how might you choose bins differently in order to reduce variance? What's the guiding principle?