Spring Theory

Common statistical procedures are spring systems at rest.

A Gaussian belief is a spring. Its negative log-density is a quadratic potential well, so stiffness is precision and stored energy is a negative log-likelihood. The estimate is wherever the forces balance. Point estimation becomes mechanical equilibrium, and on this site you can watch it settle and drag it around.

Three ways in.

• The introduction. An essay from Hooke's law to the Kalman filter, one spring at a time.
• The dictionary. Each correspondence in one table.
• The demos. Drag the masses yourself: evidence fusion, least squares, PCA, the time-series smoother, and a dozen more.