Question on Confidence Interval

[chenxia-han]

The calculation of the confidence interval as shown in the following line is $\mu \pm \frac{\sigma}{\sqrt{s}}\sqrt{2\log{\frac{1}{2\delta}}}$, which does not align with the formula in the paper. Is that because it's a one-sided confidence interval?

https://github.com/stanford-futuredata/supg/blob/master/supg/sampler/imp_sampler.py#L101

[ddkang]

I believe the exact delta that goes in changes depending on the sampler. The SamplingBounds class simply accepts a user-provided delta, e.g., here: https://github.com/stanford-futuredata/supg/blob/master/supg/selector/recall_selector.py#L98

[chenxia-han]

Thanks for the prompt reply. I also noticed that, which leads to $\mu \pm \frac{\sigma}{\sqrt{s}}\sqrt{2\log{\frac{1}{\delta}}}$. But as specified in the Algorithm 2 of SUPG, it should be $\mu \pm \frac{\sigma}{\sqrt{s}}\sqrt{2\log{\frac{1}{\frac{1}{2} \delta}}}$, right?

[ddkang]

Hmm, I will need to look into this, but I think your initial comment might be correct. We only need a one-sided interval for each bound.

[chenxia-han]

Thanks. Please let me know once you figure it out.