State Space Models¶

Notes on state-space models and their extensions, with applied writeups of factorial state-space models (fSSMs) for online skill rating.

Contents¶

• Kalman Filter — the linear-Gaussian filter and its nonlinear extensions: Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF)

Examples¶

Applied writeups built on the factorial state-space model from Duffield, Power and Rimella: A state-space perspective on modelling and inference for online skill rating:

• Football Model — a factorial SSM for predicting 2026 World Cup matches, benchmarked against Polymarket prices
• Tennis Model — a Gaussian factorial SSM for WTA match outcomes with a latent skill per player (tennis_ssm)