Online state and parameter estimation in Dynamic Generalised Linear Models

Inference for streaming time-series is tightly coupled with the problem of Bayesian on-line state and parameter inference. In this paper we will introduce Dynamic Generalised Linear Models, the class of models often chosen to model continuous and discrete time-series data. We will look at three different approaches which allow on-line estimation and analyse the results when applied to different real world datasets related to inference for streaming data. Sufficient statistics based methods delay known problems, such as particle impoverishment, especially when applied to long running time-series, while providing reasonable parameter estimations when compared to exact methods, such as Particle Marginal Metropolis-Hastings. State and observation forecasts will also be analysed as a performance metric. By benchmarking against a "gold standard" (off-line) method, we can better understand the performance of on-line methods in challenging real-world scenarios.