CUED Publications database

Sequential Inference Methods for Non-Homogeneous Poisson Processes with State-Space Prior

Li, C and Godsill, S (2021) Sequential Inference Methods for Non-Homogeneous Poisson Processes with State-Space Prior. IEEE Transactions on Signal Processing, 69. pp. 1154-1168. ISSN 1053-587X

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Abstract

The non-homogeneous Poisson process provides a generalised framework for the modelling of random point data by allowing the intensity of point generation to vary across its domain of interest (time or space). The use of non-homogeneous Poisson processes have arisen in many areas of signal processing and machine learning, but application is still largely limited by its intractable likelihood function and the lack of computationally efficient inference schemes, although some methods do exist for the batch data case. In this paper, we propose for the first time a sequential framework for intensity inference which combines the non-homogeneous model of Poisson data with continuous-Time state-space models for their time-varying intensity. This approach enables us to design efficient online inference schemes, for which we propose a novel sequential Markov chain Monte Carlo (SMCMC) algorithm, as is demanded by many applications where point data arrive sequentially and decisions need to be made with low latency. The proposed approach is compared with competing methods on synthetic datasets and tested with high-frequency financial order book data, showing in general improved performance and better computational efficiency than the main batch-based competitor algorithm, and better performance than a simple baseline kernel estimation scheme.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 29 Jan 2021 21:42
Last Modified: 13 Apr 2021 09:47
DOI: 10.1109/TSP.2021.3055373