AIDAID202 · Lectures 7–8

Lecture 7 · Continuous features

Gaussian MLE and the variance bias

For a Gaussian, MLE recovers the sample mean and uses division by n for the variance. Repeated sampling reveals the subtle bias in that variance estimator.

Predict first: Which changes more after one extreme outlier: the estimated mean, the estimated variance, or both?

One sample

μ̂MLE—
σ̂²MLE (÷ n)—
s² unbiased (÷ n−1)—
True σ²—

Repeat the whole experiment

Run repeated samples to compare the average variance estimates.