Simplified Kalman filtering for non-linear models.

Abstract: We will discuss the problem of approximate statistical inference in the hidden Markov models where the observation equations are non-linear.  We propose a Bayesian approach based on a Gaussian approximation as well as its versions suitable for  “large” problems. The proposed approach may be seen as an approximate Kalman filter which is generic in the sense that it can be used for any non-linear relationship between the hidden state and the outcome. We show how the proposed simplified Kalman filter can be used in the context of sport rating  where the skills of the players/teams are inferred from the observed outcomes of the games. We show how the well-known algorithms (such as the Elo, the Glicko, and the TrueSkill algorithms) may be seen as instances of the approach we develop. In order to clarify the conditions under which the gains of the Bayesian approach over the simpler solutions can actually materialize, we critically compare the known and the new algorithms by means of numerical examples using synthetic as well as empirical data.

Posted on Jan 5, 2023 in Seminar CMM, Seminars