We showed that the total MSE (which is a proxy for variance) of stratified sampling goes as N^(-3/2). Since the time cost per sample would not change (I believe?), does this mean that that stratified sampling efficiency improves as the number of samples is increased? Or is my reasoning flawed somewhere?

hanrahan

The MSE of all monte carlo sampling strategies decreases with more samples. You are right, most methods decrease linearly with more samples, where as stratified sampling decreases as N^(3/2).

The cost goes up linearly with the number of samples. But the cost per sample can be different with different sampling strategies. But in our case, most of the cost is in performing ray tracing not generating a sample. So the cost of uniform random sampling and stratified sampling are roughly the same. However, it is possible to use a sampling strategy where the cost of generating a sample could be very different.

In general, as you point up. The fact that the error decreases faster for stratified sampling by the cost is roughly the same, stratified sampling is often a net win.

We showed that the total MSE (which is a proxy for variance) of stratified sampling goes as N^(-3/2). Since the time cost per sample would not change (I believe?), does this mean that that stratified sampling efficiency improves as the number of samples is increased? Or is my reasoning flawed somewhere?

The MSE of all monte carlo sampling strategies decreases with more samples. You are right, most methods decrease linearly with more samples, where as stratified sampling decreases as N^(3/2).

The cost goes up linearly with the number of samples. But the cost per sample can be different with different sampling strategies. But in our case, most of the cost is in performing ray tracing not generating a sample. So the cost of uniform random sampling and stratified sampling are roughly the same. However, it is possible to use a sampling strategy where the cost of generating a sample could be very different.

In general, as you point up. The fact that the error decreases faster for stratified sampling by the cost is roughly the same, stratified sampling is often a net win.