Modeling Bivariate Geyser Eruption System with Covariate-Adjusted Recurrent Event Process

TL;DR

This paper introduces a covariate-adjusted bivariate recurrent event model using a Gumbel copula and lognormal marginals to analyze Yellowstone geyser eruptions, providing insights into their interdependence and covariate effects.

Contribution

It develops a novel parametric bivariate recurrent event model with covariate adjustment and applies it to geyser eruption data, enhancing understanding of interdependent event systems.

Findings

Model effectively captures geyser eruption interdependence.

Covariates significantly influence eruption timing.

Simulation validates model performance.

Abstract

Geyser eruption is one of the most popular signature attractions at the Yellowstone National Park. The interdependence of geyser eruptions and impacts of covariates are of interest to researchers in geyser studies. In this paper, we propose a parametric covariate-adjusted recurrent event model for estimating the eruption gap time. We describe a general bivariate recurrent event process, where a bivariate lognormal distribution and a Gumbel copula with different marginal distributions are used to model an interdependent dual-type event system. The maximum likelihood approach is used to estimate model parameters. The proposed method is applied to analyzing the Yellowstone geyser eruption data for a bivariate geyser system and offers a deeper understanding of the event occurrence mechanism of individual events as well as the system as a whole. A comprehensive simulation study is conducted to evaluate the performance of the proposed method.