Using hidden multi-state Markov models with multi-parameter volcanic data to provide empirical evidence for alert level decision-support

For the purposes of eruption forecasting and hazard mitigation, a volcanic crisis may be represented as a staged progression of states of unrest, each with its own timescale and likelihood of transition to other states (or to climactic eruption). If the state conditions can be interpreted physically, e.g., in terms of advancing materials failure, this knowledge could be used directly to inform decisions on alert level setting. A multi-state Markov process provides one simple model for defining states and for estimating rates of switching between states. However, for eruptive processes, such states are not directly observable and must be inferred from latent markers, such as seismic activity, gas output, deformation rates, etc., some of which may be contradictory. Interpretations of uncertain data will be liable to error, so a model is needed which can simultaneously estimate both elements: the transition likelihood of a hidden process and the probabilities of state misclassification. We describe the concept and underlying principles of continuous-time hidden Markov models and demonstrate them in a decision-support context with a preliminary working implementation using MULTIMO data. Where multi-parameter streams of raw, processed or conditioned data of different kinds are available, these can be input in near real-time to appropriate hidden multi-state Markov models, the outputs of each providing their own objective analyses of eruptive state in probabilistic terms. These separate, multiple indicators of state can then be input into a Bayesian Belief Network framework for weighing and combining them as different strands of evidence, together with other observations, data, interpretations and expert judgment.