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

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