Alternating Gaussian Process Modulated Renewal Processes for Modeling Threshold Exceedances and Durations.

Area of Science:

• Environmental Science
• Statistical Modeling
• Time Series Analysis

Background:

• Environmental monitoring often requires modeling the timing and duration of threshold exceedances.
• Continuous time data can be viewed as an alternating renewal process with states above and below a threshold.

Purpose of the Study:

• To develop a flexible statistical model for analyzing threshold exceedance events in environmental data.
• To incorporate temporal dynamics and spatial variation using Gaussian processes.
• To enable computationally feasible model fitting for long time series.

Main Methods:

• Utilized a two-state continuous time Markov process (alternating renewal process).
• Employed Gaussian process modulation for state-specific intensity functions.
• Adopted the nearest neighbor Gaussian process (NNGP) for computational tractability.
• Applied a Bayesian framework for model fitting and inference.

Main Results:

• Developed a Gaussian process-modulated renewal process applicable to environmental monitoring.
• Implemented NNGP to overcome computational challenges with long time windows.
• Successfully applied the model to hourly ozone data from four US sites.
• Generated estimated time-varying intensity profiles for threshold crossings.

Conclusions:

• The proposed model effectively captures the dynamics of environmental threshold exceedances.
• The NNGP approach allows for scalable and efficient analysis of large environmental datasets.
• Inference on exceedance duration, frequency, and state occupancy was achieved.