Current urban air pollution is a major environmental risk to population health. Much of the evidence on air pollution and its eects are based on studies focused on a single pollutant, where co-pollutants are treated as confounders or modifying factors. In reality, polluted air exists as a complex mixture of particles, gases and toxic substances and people experience a simultaneous exposure to multiple pollutants and sources. This thesis is concerned with statistical methods for characterising exposure metrics of airborne particulate matter (PM) and sources within a time series framework. Two original Bayesian modelling approaches are presented, with application to real-world data and inference based on Markov Chain Monte Carlo methods. A hierarchical modelling approach, which incorporates temporal and spatial statistical structures, was developed for estimating and predicting short-term concentrations of particles from dierent sources in an urban environment. Taking advantage of a varying coecient model, this approach modelled the long-range transport of the secondary PM and local primary components, combining observed concentrations from monitoring networks with output from a local-scale dispersion model, while accounting for factors with direct or indirect inuence on the particle distribution and formation. A semiparametric model, based on a Dirichlet process mixture model dened by a stick-breaking construction, was proposed for clustering time points with similar particle and health response proles. This model used a one-step procedure for dimension reduction and regression, while adjusting for aspects associated with time variation such as trend and seasonality through smooth functions. It also provided a tool to assess the changes in health eects from various policies to control ambient PM. These models are exible and reproducible in dierent environmental contexts, and were able to capture dependencies in real data and predict temporal and spatio-temporal responses with associated uncertainty.