Geostatistical estimation and prediction for censored responses

Area of Science:

• Environmental Science
• Geostatistics
• Statistical Modeling

Background:

• Environmental data frequently contains values below quantifiable detection limits, leading to censored measurements.
• Current statistical methods for handling censored data often involve arbitrary choices, potentially compromising inference accuracy.
• Existing ad hoc methods like data augmentation or arbitrary limit selection can lead to imprecise results in geostatistical analysis.

Purpose of the Study:

• To develop an exact maximum likelihood estimation framework for geostatistical models with censored data.
• To introduce a novel application of the Stochastic Approximation of the Expectation Maximization (SAEM) algorithm for parameter estimation under censoring.
• To provide improved inference and prediction capabilities for environmental datasets with detection limits.

Main Methods:

• Utilized an exact maximum likelihood estimation approach.
• Applied the Stochastic Approximation of the Expectation Maximization (SAEM) algorithm for parameter and variance component estimation.
• Validated the method through simulation studies and a real-world application involving arsenic concentration data.

Main Results:

• The proposed SAEM-based method demonstrated superior performance compared to traditional techniques.
• The method showed improved finite sample properties for parameter estimates and enhanced prediction accuracy.
• The approach proved robust and effective for analyzing censored environmental data, as shown with arsenic concentration.

Conclusions:

• The novel SAEM algorithm provides an exact and elegant solution for statistical inference and prediction with censored geostatistical data.
• This method offers a more robust and precise alternative to existing ad hoc techniques for environmental data analysis.
• The associated R package, CensSpatial, facilitates the implementation of these advanced statistical methods.