Shahzadi, Amina

Estimating record completeness using a 2-state hidden Markov model

Amina Shahzadi¹, Ting Wang¹, Matthew Parry¹, and Mark Bebbington²

1. Department of Mathematics and Statistics, University of Otago, Dunedin

2. Institute of Fundamental Sciences, Massey University, Palmerston North

Natural phenomena such as earthquakes and volcanic eruptions can cause catastrophic damage. Such phenomena can be modelled using point processes. A major problem related to point process modelling of the earthquake and volcanic eruption data, however, is an underestimation of hazard caused by missing data. In particular, the number of missing observations between each pair of consecutively observed events in such type of records is unknown. Modelling volcanic eruptions as a renewal process, we develop a hidden Markov model (HMM) to tackle the problem with missing data in volcanic eruption records. In this model, the states of the hidden process correspond to whether or not there is one or more missing event(s) between each pair of consecutively observed events. We, therefore, propose a two-state model, where state 1 represents no missing observation, and state 2 represents that there is a variable, unknown, number of missing observations between a pair of consecutively observed events in the observed record. We model the number of missing observations in state 2 as a Poisson variable. The inter-arrival times of the observed process are assumed to have a gamma distribution in state 1, and a compound Poisson-gamma distribution in state 2. We apply this model to a global volcanic eruption record and demonstrate how we estimate the completeness of the record and the future hazard rate.

This presentation is eligible for the NZSA Student Prize.