Modeling temporally misaligned data across space: The case of total pollen concentration in Toronto

Due to the high costs of monitoring environmental processes, measurements are commonly taken at different temporal scales. When observations are available at different temporal scales across different spatial locations, we name it temporal misalignment. Rather than aggregating the data and modeling it at the coarser scale, we propose a model that accounts simultaneously for the fine and coarser temporal scales. More specifically, we propose a spatiotemporal model that accounts for the temporal misalignment when one of the scales is the sum or average of the other by using the properties of the multivariate normal distribution. Inference is performed under the Bayesian framework, and uncertainty about unknown quantities is naturally accounted for. The proposed model is fitted to data simulated from different spatio-temporal structures to check if the proposed inference procedure recovers the true values of the parameters used to generate the data. The motivating example consists of measurements of total pollen concentration across Toronto, Canada. The data were recorded daily for some sites and weekly for others. The proposed model estimates the daily measurements at sites where only weekly data was recorded and shows how the temporal aggregation of the measurements affects the associations with different covariates.