Sequential Bayesian Inference for Dynamic Linear Models of Sensor Data

Abstract

We develop a spatio-temporal model to analyse pairs of observations on temperature and humidity. The data consist of six months of observations at five locations collected from a sensor network deployed in North East England. The model for the temporal component takes the form of two coupled dynamic linear models (DLMs), specified marginally for temperature and conditionally for humidity given temperature. To account for dependence at nearby locations, the governing system equations include spatial e ects, specified using a Gaussian process. To understand the stochastic nature of the data, we perform fully Bayesian estimation for the model parameters and check the model fit via posterior distributions. The intractability of the posterior distribution necessitates the use of computationally intensive methods such as Markov chain Monte Carlo (MCMC). The main disadvantage of MCMC is computational ine ciency when dealing with large datasets. Therefore, we exploit a class of sequential Monte Carlo (SMC) algorithms known as particle filters, which sequentially approximate the posterior through a series of reweighting and resampling steps. The tractability of the observed data likelihood under the DLM admits the implementation of an iterated batch importance sampling (IBIS) scheme, which additionally uses a resample-move step to circumvent the particle degeneracy problem. To alleviate the computational burden brought from the resample-move step of IBIS, we develop a novel online version of IBIS by modifying the resample-move step through approximating the posterior over an observation window whose pre-specified length trades o accuracy and computational cost. Furthermore, performing the resampling step independently for batches of parameter samples allows a parallel implementation of the algorithm to be performed on a powerful multi-core high performance computing system. A comparison of observed measurements with their one-step and two-step forecast distributions shows that the model provides a good description of the underlying process and provides reasonable forecast accuracy.