Bayesian inference with application to air quality monitoring

Lead Research Organisation: Imperial College London
Department Name: Dept of Mathematics

Abstract

This project aims to develop new methodology for performing statistical inference in environmental modelling applications. These applications require the use of a large number of sensors that collect data frequently and are distributed over a large region in space. This motivates the use of a space time varying stochastic dynamical model, defined in continuous time via a (linear or non-linear) stochastic partial differential equation, to model quantities such as air quality, pollution level, and temperature. We are naturally interested in fitting this model to real data and, in addition, on improving on the statistical inference using a carefully chosen frequency for collecting observations, an optimal sensor placement, and an automatic calibration of sensor biases. From a statistical perspective, these problems can be formulated using a Bayesian framework that combines posterior inference with optimal design.

Performing Bayesian inference or optimal design for the chosen statistical model may be intractable, in which case the use of simulation based numerical methods will be necessary. We aim to consider computational methods that are principled but intensive, and given the additional challenges relating to the high dimensionality of the data and the model, must pay close attention to the statistical model at hand when designing algorithms to be used in practice. In particular, popular methods such as (Recursive) Maximum Likelihood, Markov Chain Monte Carlo, and Sequential Monte Carlo, will need to be carefully adapted and extended for this purpose.

Publications

10 25 50

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/R512540/1 01/10/2017 30/09/2021
1925152 Studentship EP/R512540/1 01/10/2017 30/09/2021 Louis Sharrock