# Accession Number:

## ADP013737

# Title:

## Generalised Gauss-Markov Regression

# Descriptive Note:

## Conference paper

# Corporate Author:

## NATIONAL PHYSICAL LAB TEDDINGTON (UNITED KINGDOM)

# Personal Author(s):

# Report Date:

## 2001-07-01

# Pagination or Media Count:

## 8.0

# Abstract:

Experimental data analysis is an key activity in metrology, the science of measurement. It involves developing a mathematical model of the physical system in terms of mathematical equations involving parameters that describe all the relevant aspects of the system. The model specifies how the system is expected to respond to input data and the nature of the uncertainties in the inputs. Given measurement data, estimates of the model parameters are determined by solving the mathematical equations constructed as part of the model, and this requires developing an algorithm or estimator to determine values for the parameters that best explain the data. In many cases, the parameter estimates are given by the solution of a least-squares problem. This paper discusses how various uncertainty structures associated with the measurement data can be taken into consideration and describes the algorithms used to solve the resulting regression problems. Two applications from NPL are described which require the solution of generalised distance regression problems the use of measurements of primary standard natural gas mixtures to estimate the composition of a new natural gas mixture, and the analysis of calibration data to estimate the effective area of a pressure balance.

# Descriptors:

# Subject Categories:

- Numerical Mathematics
- Test Facilities, Equipment and Methods
- Statistics and Probability