Statistics
Maximum Likelihood
Given data, which bell curve most likely produced it? Slide the mean and spread of a Gaussian and watch the likelihood of the sample rise and fall. The best fit is no accident: it lands exactly on the sample's own mean and spread.
Log-likelihood—
Sample mean—
Sample std—
What to observe
- Each vertical stick is one data point's likelihood: how tall the bell sits above it. The total (log-)likelihood adds them up. Drag μ and σ to make the curve sit as high as possible over the data.
- Hit Snap to best fit. The maximum-likelihood μ is exactly thesample mean, and the best σ is the sample standard deviation. Maximizing likelihood re-derives the formulas you already know.
- The mini-plot is the log-likelihood as you slide μ. It is a smooth hill with a single peak, which is why gradient ascent (and every trained model) can climb straight to it.
Shortcuts: space run/pause · s step · r reset · f fullscreen