A Dynamic Approach to Linear Statistical Calibration with an Application in Microwave Radiometry

TL;DR

This paper introduces a dynamic Bayesian approach using Dynamic Linear Models for statistical calibration, allowing for real-time monitoring of instrument drift, and demonstrates its effectiveness through simulations and microwave radiometry data.

Contribution

It presents a novel dynamic calibration method employing Bayesian DLMs to model time-varying parameters, improving calibration accuracy over static models.

Findings

Dynamic calibration outperforms static methods at various noise levels.

Bayesian DLMs provide better uncertainty quantification.

Application to microwave radiometry data shows practical effectiveness.

Abstract

The problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the 'classical' approach and the 'inverse' regression approach. Both of these models are static models and are used to estimate exact measurements from measurements that are affected by error. In the engineering context, the variables of interest are considered to be taken at the time at which you observe it. The Bayesian time series analysis method of Dynamic Linear Models (DLM) can be used to monitor the evolution of the measures, thus introducing an dynamic approach to statistical calibration. The research presented employs the use of Bayesian methodology to perform statistical calibration. The DLM's framework is used to capture the time-varying parameters that maybe changing or drifting over time. Two separate DLM based models are presented in this paper. A simulation study is conducted where the two models are compared to some well known 'static' calibration approaches in the literature from both the frequentist and Bayesian perspectives. The focus of the study is to understand how well the dynamic statistical calibration methods performs under various signal-to-noise ratios, r. The posterior distributions of the estimated calibration points as well as the 95% coverage intervals are compared by statistical summaries. These dynamic methods are applied to a microwave radiometry data set.