Bayesian hierarchical modeling and prediction of zero-inflated continuous-valued data using two environmental-monitoring networks

Researchers use spatio-temporal modeling to build statistical models that vary across time and space. The data set used in this paper is about rainfall measured by two different networks — the Community Collaborative Rain, Hail & Snow Network (CoCoRaHS) and the National Weather Service (NWS). The CoCoRaHS network is a big data set of civilian gathered rain data. The NWS is a much smaller network of rain gauges that we believe to be more reliable than the civilian gathered complement. These two networks contributed rainfall measurements that we intended to model with spatio-temporal techniques.

The main idea behind a spatio-temporal model is that two points that are close together are going to be more correlated than two points that are far away. This includes distances measured in time as well as distances measured in space. For example, the amount of rainfall one person receives is much more similar to their neighbor than some faraway stranger. Analogously, the rainfall for two subsequent days is going to be much more similar than the rainfall for two days that are a week apart. This intuitive idea about the correlation between space and time is the driving force in the theory behind spatio-temporal modeling.

A further complication when building the model is that rainfall is “zero-inflated.” This means that there is an unexpectedly large amount of sites that have no rainfall. The zero-inflated data was dealt with using a censored model where large chunks of censored probability were used to estimate zeros in our data.

The model that we built incorporates all three of these difficulties — two monitoring networks, spatio-temporal modeling, and zero-inflated data. The low predictive error that we calculate at the end demonstrates the importance of factoring in each of these issues.