Exploring Continuous Bayesian Network Modelling for Eruption Forecasting

New Zealand best practice recommendations for volcano observatories propose using probabilistic methods with uncertainties to forecast eruptions. Bayesian networks (BNs) are probabilistic graphical models that have been promoted in the literature for more than a decade as a framework for combining different volcano monitoring data and linking them to the underlying driving processes when forecasting eruptions. However, applications of BNs in real-time volcano monitoring are rare.  

The graphical part of BNs represents the modelled variables as nodes that are connected by arrows pointing from a parent to a child node. The probabilistic part of BNs describes the joint probability distribution of all variables. Most commonly, the random variables are modelled as discrete with a finite number of states (e.g. low, medium, high , or increasing, unchanged, decreasing) that are mutually exclusive, and must exhaustively describe the possible node states. The dependencies between discrete variables are captured in Conditional Probability Tables (CPTs). The CPT size increases with the number of parent nodes and the number of (parents and child) nodes’ states. Some of the conditions might be very rare, making it impossible to populate the CPT robustly.  

Volcano monitoring data are often continuous and it can be challenging to define boundaries between states. We recently developed a discrete BN to forecast volcanic eruption on Mt Ruapehu, Aotearoa New Zealand. The model structure was defined by experts, and the CPTs were estimated from the long monitoring records, supplemented by expert elicitation. Here we use the same model structure and data to explore continuous methods of model parameterisation. We model the probability distribution of each variable separately from the dependence and parameterise the dependence using (conditional) rank correlations. This approach is implemented in the Uninet software, which has great features for data analysis that help us present the data in novel ways.