Quantifying predictive uncertainty inherent in the nonlinear multivariate dependence structure of multi-step-ahead PM2.5 forecasts is challenging. This study integrates a Multivariate Bayesian Uncertainty Processor (MBUP) and an artificial neural network (ANN) to make accurate probabilistic PM2.5 forecasts. The contributions of the proposed approach are two-fold. First, the MBUP can capture the nonlinear multivariate dependence structure between observed and forecasted data. Second, the MBUP can alleviate predictive uncertainty encountered in PM2.5 forecast models that are configured by ANNs. The reliability of the proposed approach was assessed by a case study on air quality in Taipei City of Taiwan. We consider forecasts of PM2.5 concentrations as a function of meteorological and air quality factors based on long-term (2010–2018) hourly observational datasets. Firstly, the Back Propagation Neural Network (BPNN) and the Adaptive Neural Fuzzy Inference System (ANFIS) were investigated to produce deterministic forecasts. Results revealed that the ANFIS model could learn different air pollutant emission mechanisms (i.e. primary, secondary and natural processes) from the clustering-based fuzzy inference system and produce more accurate deterministic forecasts than the BPNN. The ANFIS model then provided inputs (i.e. point estimates) to probabilistic forecast models. Next, two post-processing techniques (MBUP and the Univariate Bayesian Uncertainty Processor (UBUP)) were separately employed to produce probabilistic forecasts. The Bayesian Uncertainty Processors (BUPs) can model the dependence structure (i.e. posterior density function) between observed and forecasted data using a prior density function and a likelihood density function. Here in BUPs, the Monte Carlo simulation was introduced to create a probabilistic predictive interval of PM2.5 concentrations. The results demonstrated that the MBUP not only outperformed the UBUP but also suitably characterized the complex nonlinear multivariate dependence structure between observations and forecasts. Consequently, the proposed approach could reduce predictive uncertainty while significantly improving model reliability and PM2.5 forecast accuracy for future horizons.
