Sequential Bayesian computation of logistic regression models

The extended Kalman filter (EKF) algorithm for identification of a state space model is shown to be a sensible tool in estimating a logistic regression model sequentially. A Gaussian probability density over the parameters of the logistic model is propagated on a sample by sample basis. Two other approaches, the Laplace approximation and the variational approximation are compared with the state space formulation. Features of the latter approach, such as the possibility of inferring noise levels by maximising the “innovation probability” are indicated. Experimental illustrations of these ideas on a synthetic problem and two real world problems are discussed