How is the reported confidence interval constructed from the importance-sampling estimates?

Conditions

• Uses the sample standard deviation of the weighted estimates.
• The interval is presented as a numerical summary based on a normal approximation.

Reasoning, step by step

1. Compute the sample standard deviation of the weighted estimator array.
2. Divide the standard deviation by the square root of the number of samples.
3. Multiply the result by 1.96 to get the half-width.
4. Add and subtract the half-width from the point estimate to get the bounds.

Example

The code computes `oHat = ests.std()` and `widthCI = 1.96 * oHat / np.sqrt(R)`, then prints bounds as `lHat-widthCI` and `lHat+widthCI`.

Common misconceptions

• Assuming `widthCI` represents the full width of the interval rather than the half-width.
• Believing the interval is asymmetric.

Watch the explanation

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