Fitting an AR(1) Model to Environmental Measurements with Non-Detects

• Activity Number: 195
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): John Rogers*+
• Keywords: Time series ; Bayesian ; survival analysis ; measurement error

Abstract

For concentration measurements, the detection limit (DL) is a small concentration below which, due to measurement error, a measurement is not statistically different from zero. Non-detects are measurements reported as below the detection limit (e.g., < 5), resulting in censored data. In many situations, the measurement distribution can be described as the sum of a lognormal distributed concentration and a normally distributed measurement error. The data may be modeled by replacing the non-detects by substitute values, such as DL/2, or using survival analysis assuming a lognormal distribution. Environmental time-series can often be approximated by an AR(1) time-series model for the log-transformed concentrations. However, time series models do not account for non-detects. Bayesian procedures provide adequate flexibility to fit time-series models to data with non-detects, whether assuming the concentration distribution is lognormal or the sum of a normal and lognormal distribution. This paper illustrates a Bayesian approach to fit water pollution data with non-detects and provides simulation results comparing the Bayesian fit to some simpler approximations.