Certainty and Assumptions, a talk by Alistair Forbes (National Physical Laboratory)
Abstract
Abraham Maslow: If the only tool we have is a hammer, all problems tend to look like nails.
George Box: All models are wrong, but some models are useful.
Donald Rumsfeld: There are known knowns and known unknowns. But there are also unknown unknowns.
The National Physical Laboratory is the UK’s National Metrology Institute (NMI), responsible for ensuring that all measurement in the UK can be made traceable to standard units, e.g. to the metre, etc. A measurement result is traceable only if it is associated with an uncertainty statement. All uncertainty statements are derived from an underlying model of the measurement system describing the functional relationship between the various variables and the statistical characterisation associated with the measurements.
The Guide to the Expression of Uncertainty in Measurement (the GUM) provides a methodology for evaluating measurement uncertainty. It starts with an input-output model Y = f(X) in which the measured Y is expressed as a function of influence quantities X. Once a probability distribution p(X) is assigned to X, the distribution p(Y) for Y is defined. Uncertainties associated with X are propagated forward through the model to determine the uncertainty associated with Y and there are straightforward computational tools for performing this type of uncertainty propagation.
The current uncertainty propagation methodologies used by NMIs assume i) the input-output model Y = f(X) exists, ii) that the function f is known with certainty and iii) the distributions associated to X are known with certainty. In practice, all three assumptions can be challenged. Measurement problems naturally arise as inverse problems and, in order to apply the uncertainty propagation tools, have to be reformulated to look like forward problems. Models are often approximations or have empirical components that try to account for our lack of complete knowledge of the underlying physical system. Distributions are often assigned on the basis of assumptions of normality, independence and expert judgement.
In this talk, I will discuss some of the newer uncertainty quantification tools that enable us to arrive at more comprehensive uncertainty statements that are based on a more realistic assessment of what we know, what we don’t know or even what we don’t know we don’t know.
Alistair Forbes joined the National Physical Laboratory in 1985 after studying mathematics at the universities of Aberdeen, Newcastle upon Tyne and Pennsylvania. He is a Fellow in the Mathematics and Modelling Group and Science Area Leader for Data Science and Uncertainty Quantification. He is a Member of the IMA, a Chartered Mathematician, a fellow of the Royal Statistical Society and Visiting Professor at the University of Huddersfield.
No charge is made to attend meetings and non-members are welcome.
