Mathematics
Bayesian Inference with Conjugate Priors for Streaming Data
Quick fact
With conjugate priors, Bayesian updating is so simple that the posterior can be computed using just a few summary numbers (sufficient statistics), making it possible to update models in constant time regardless of how many data points have been seen.
Why this is interesting
Imagine a weather app that updates its forecast probability of rain every time new sensor data arrives—how can it keep learning without recomputing everything from scratch?