Abstract
Hidden Markov models (HMMs), especially those with a Poisson density governing the latent state-dependent emission probabilities, have enjoyed substantial and undeniable success in modeling natural hazards. Classifications among these hazards, induced through quantifiable properties such as varying intensities or geographic proximities, often exist, enabling the creation of an empirical recurrence rates ratio (ERRR), a smoothing statistic that is gradually gaining currency in modeling literature due to its demonstrated ability in unearthing interactions. Embracing these tools, this study puts forth a refreshing monitoring alternative where the unobserved state transition probability matrix in the likelihood of the Poisson based HMM is replaced by the observed transition probabilities of a discretized ERRR. Analyzing examples from Hawaiian volcanic and West Atlantic hurricane interactions, this work illustrates how the discretized ERRR may be interpreted as an observed version of the unobserved hidden Markov chain that generates one of the two interacting processes. Surveying different facets of traditional inference such as global state decoding, hidden state predictions, one-out conditional distributions, and implementing related computational algorithms, we find that the latest proposal estimates the chances of observing a high-risk period, one threatening several hazards, more accurately than its established counterpart. Strongly intuitive and devoid of forbidding technicalities, the new prescription launches a vision of surer forecasts and stands versatile enough to be applicable to other types of hazard monitoring (such as landslides, earthquakes, floods), especially those with meager occurrence probabilities.
Highlights
Hidden Markov models (HMMs), especially those with a Poisson density governing the latent statedependent emission probabilities, have enjoyed substantial and undeniable success in modeling natural hazards
If it can be assumed that the observations tracking the series of interest are generated by probability distributions relying on some underlying latent states, and that the state space is equipped with the one-step Markov property described previously, the resulting framework is known as a hidden Markov model (HMM)
The count-based examples we have sampled from volcanology and weather science serve as proper instances on which to implement both the Poisson-HMM and empirical recurrence rates ratio (ERRR)-HMM techniques
Summary
Hidden Markov models (HMMs), especially those with a Poisson density governing the latent statedependent emission probabilities, have enjoyed substantial and undeniable success in modeling natural hazards Classifications among these hazards, induced through quantifiable properties such as varying intensities or geographic proximities, often exist, enabling the creation of an empirical recurrence rates ratio (ERRR), a smoothing statistic that is gradually gaining currency in modeling literature due to its demonstrated ability in unearthing interactions. Embracing these tools, this study puts forth a refreshing monitoring alternative where the unobserved state transition probability matrix in the likelihood of the Poisson based HMM is replaced by the observed transition probabilities of a discretized ERRR. The last contains some concluding observations and remarks on how this work may prosper
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