A unified approach to statistical estimation and model parameterisation in mass calibration

Abstract

This thesis presents a unified and homogenous system of data analysis and parameter estimation. The process is applied to mass determination but the underlying principles are general and the philosophy applies to any data reduction process. Two main areas are covered: uncertainty analysis via the recommendations of the ISO Guide and secondly parameter estimation of over-determined measurement systems. Application to mass determination of the ISO-recommended procedures and also parameter estimation in mass calibration have'been treated previously. What is done here is an innovative attempt to link these two areas together by focusing on the measurement philosophy underlying each and producing a Unified Approach to parameter estimation in mass determination. A unique feature is the application of the ideas of classical probability theory to uncertainty analysis and mass metrology, particular emphasis being placed on employing a consistent and logically coherent analysis. Criteria of consistency from classical probability theory are used as a basis for much of the work, and some useful definitions with respect to subjective information and unbiased analysis are presented which form a useful contribution to the metrology of uncertainty theory. With respect to parameter estimation techniques novel methods recently proposed in the literature are investigated on a mathematical level and it is shown that the minimum variance estimator used is in fact an application of Bayesian techniques to parameter estimation. This provides a useful link to the ISO Guide on uncertainty analysis, which is mathematically based on a Bayesian view of probability. The traditional least squares method of parameter estimation which has been previously shown to be internally inconsistent in its view of the reference information, is shown in this work to be incompatible with the ISO Guidelines and the consistency criteria mentioned above. The benefits of applying the Unified Approach are amply seen in the improved estimates and lower covariances achievable with the Bayesian estimators. The capabilities of Bayesian estimators are explored in some detail with experimental data. This provides some new insight into the estimation technique and discusses how robustly it can deal with inaccurate data and also attempts to quantify the maximum improvement in uncertainty that is achievable through recalibration and sequential estimation with this method. The conclusion reached is that a Bayesian view of probability, without the restriction of maintaining a separation between random and systematic uncertainties leads to a much improved system of data analysis