The 'Guide to the Expression of Uncertainty in Measurement' (GUM) requires that the way a measurement uncertainty is expressed should be transferable. It should be possible to use directly the uncertainty evaluated for one measurement as a component in evaluating the uncertainty for another measurement that depends on the first. Although the method for uncertainty evaluation described in the GUM meets this requirement of transferability, it is less clear how this requirement is to be achieved when GUM Supplement 1 is applied. That Supplement uses a Monte Carlo method to provide a sample composed of many values drawn randomly from the probability distribution for the measurand. Such a sample does not constitute a convenient way of communicating knowledge about the measurand. In this paper consideration is given to obtaining a more compact summary of such a sample that preserves information about the measurand contained in the sample and can be used in a subsequent uncertainty evaluation. In particular, a coverage interval for the measurand that corresponds to a given coverage probability is often required. If the measurand is characterized by a probability distribution that is not close to being Gaussian, sufficient information has to be conveyed to enable such a coverage interval to be computed reliably.A quantile function in the form of an extended lambda distribution can provide adequate approximations in a number of cases. This distribution is defined by a fixed number of adjustable parameters determined, for example, by matching the moments of the distribution to those calculated in terms of the sample of values. In this paper, alternative flexible models for the quantile function and methods for determining a quantile function from a sample of values are proposed for meeting the above needs.

The European Metrology Research Programme (EMRP) is funding project EMRP-NEW04 on novel mathematical and statistical approaches to uncertainty evaluation. Technical areas covered by the project include uncertainty evaluation for inverse problems, regression, computationally expensive models, and decision-making and conformity assessment. Here we describe the work to be carried out in each technical area, including an introduction to the application case-studies used within the project.

We introduce a software simulation tool that can be used to study the measurement performance (both actual and intended) of sensor networks. The software, which is publicly available, is written in Matlab (R) with data read from an Excel (R) workbook, and may be used to investigate network performance, to compare different data fusion algorithms, and to evaluate the measurement uncertainties associated with aggregated data from networks.The software can be used to simulate networks in which sensors are intermittently faulty or unreliable, varying levels of noise appear in the sensor outputs, and the sensor outputs possess interdependencies, that is, the response of one class of sensor depends on the quantity being measured by another class of sensor.We set out a detailed account of our mathematical approach to simulating sensor networks and to data fusion and discuss briefly key features of the examples included with the software. We make recommendations for good practice in network design and choice of data fusion algorithm based on the examples, and discuss some of the limitations of our approach to data fusion applied to time series measurements. Crown Copyright (C) 2013 Published by Elsevier Ltd. All rights reserved.

Numerical quantification of the results from a measurement uncertainty computation is considered in terms of the inputs to that computation. The primary output is often an approximation to the PDF (probability density function) for the univariate or multivariate measurand (the quantity intended to be measured). All results of interest can be derived from this PDF. We consider uncertainty elicitation, propagation of distributions through a computational model, Bayes’ rule and its implementation and other numerical considerations, representation of the PDF for the measurand, and sensitivities of the numerical results with respect to the inputs to the computation. Speculations are made regarding future requirements in the area and relationships to problems in uncertainty quantification for scientific computing.

OBJECTIVE:To investigate the relationship between acute-phase serum amyloid A (A-SAA) and joint destruction in inflammatory arthritis.METHODS:Serum A-SAA and C-reactive protein (CRP) levels, the erythrocyte sedimentation rate (ESR), and levels of matrix metalloproteinase 1 (MMP-1), MMP-2, MMP-3, MMP-9, MMP-13, tissue inhibitor of metalloproteinases 1 (TIMP-1), vascular endothelial growth factor (VEGF), and type I and type II collagen-generated biomarkers C2C and C1,2C were measured at 0-3 months in patients with inflammatory arthritis commencing anti-tumor necrosis factor α (anti-TNFα) therapy and were correlated with 1-year radiographic progression. The effects of A-SAA on MMP/TIMP expression on RA fibroblast-like synoviocytes (FLS), primary human chondrocytes, and RA/psoriatic arthritis synovial explant cultures were assessed using real-time polymerase chain reaction, enzyme-linked immunosorbent assay, antibody protein arrays, and gelatin zymography.RESULTS:Serum A-SAA levels were significantly (P < 0.05) correlated with MMP-3, the MMP-3:TIMP-1 ratio, C1,2C, C2C, and VEGF. The baseline A-SAA level but not the ESR or the CRP level correlated with the 28-joint swollen joint count and was independently associated with 1-year radiographic progression (P = 0.038). A-SAA increased MMP-1, MMP-3, MMP-13, and MMP/TIMP expression in RA FLS and synovial explants (P < 0.05). In chondrocytes, A-SAA induced MMP-1, MMP-3, and MMP-13 messenger RNA and protein expression (all P < 0.01), resulting in a significant shift in MMP:TIMP ratios (P < 0.05). Gelatin zymography revealed that A-SAA induced MMP-2 and MMP-9 activity. Blockade of the A-SAA receptor SR-B1 (A-SAA receptor scavenger receptor-class B type 1) inhibited MMP-3, MMP-2, and MMP-9 expression in synovial explant cultures ex vivo. Importantly, we demonstrated that A-SAA has the ability to induce TNFα expression in RA synovial explant cultures (P < 0.05).CONCLUSION:A-SAA may be involved in joint destruction though MMP induction and collagen cleavage in vivo. The ability of A-SAA to regulate TNFα suggests that A-SAA signaling pathways may provide new therapeutic strategies for the treatment of inflammatory arthritis.

The measurement of the severity of electric light flicker is achieved using a complex model of the human response embodied in a flickermeter. The complex nature of the model leads to variations in flicker readings with voltage input that can be hard to predict. Uncertainty evaluation is therefore difficult to achieve by conventional methods, and a Monte Carlo approach is required. This paper describes the implementation of such an approach to evaluate the uncertainty for flicker measurements based on a model of the measurement.

Optimisation techniques are commonly used for parameter estimation in a wide variety of applications. The application described here is a laser flash thermal diffusivity experiment on a layered sample where the thermal properties of some of the layers are unknown. The aim is to estimate the unknown properties by minimising, in a least squares sense, the difference between model predictions and measured data. Two optimisation techniques have been applied to the problem. Results suggest that the classical nonlinear least-squares optimiser is more efficient than particle swarm optimisation (PSO) for this type of problem. Results have also highlighted the importance of defining a suitable objective function and choosing appropriate model parameters.

This report describes work carried out to determine the thermal conductivity of an oxide layer on a sample by using optimisation techniques to minimise the difference between measured data and the results of a continuous model.

Resource-constrained embedded systems such as wireless sensor networks are becoming increasingly sought-after in a range of critical sensing applications. Hardware for such systems is typically developed as a general tool, intended for research and flexibility. These systems often have unexpected limitations and sources of error when being implemented for specific applications. We investigate via measurement and simulation the output of the onboard clock of a Crossbow MICAz testbed, comprising a quartz oscillator accessed via a combination of hardware and software. We show that the clock output available to the user suffers a number of instabilities and errors. Using a simple software simulation of the system based on a series of nested loops, we identify the source of each component of the error, finding that there is a 7.5 × 10−6 probability that a given oscillation from the governing crystal will be miscounted, resulting in frequency jitter over a 60 µHz range.

OBJECTIVETo investigate whether short-term changes in serum biomarkers of type II collagen degradation (C2C) and types I and II collagen degradation (C1,2C), as well as the biomarker for the synthesis of type II procollagen (CPII) can predict radiographic progression at 1 year following initiation of biologic therapy in patients with inflammatory arthritis.METHODSSerum levels of biomarkers were measured at baseline and at 1, 3, 6, 9, and 12 months after initiation of biologic therapy. A composite score reflecting changes from baseline in all 3 biomarkers (DeltaCOL) was calculated. Associations with clinical responses according to the 28-joint count Disease Activity Score and with radiographic progression according to the modified Sharp/van der Heijde score (SHS) were assessed.RESULTSThe 1-year increase in the SHS correlated with the 1-month change in C2C results (r = 0.311, P = 0.028) and the DeltaCOL score (r = 0.342, P = 0.015). Radiographic progression was predicted by increases in serum C2C at 1 month (P = 0.031). The DeltaCOL score was significantly associated with 1-year radiographic progression after 1 (P = 0.022), 3 (P = 0.015), 6 (P = 0.048), and 9 (P = 0.019) months of therapy. Clinical remission was predicted by 1-month decreases in serum levels of C2C (P = 0.008) and C1,2C (P = 0.036). By regression analysis, 1-month changes in C2C, C1,2C, and CPII levels were independently associated with, and correctly predicted radiographic outcome in, 88% of the patients.CONCLUSIONShort-term changes in serum levels of collagen biomarkers following initiation of biologic therapy may better predict long-term clinical and radiographic outcomes. These collagen biomarkers may therefore be valuable new early indicators of short-term biologic treatment efficacy in clinical trials and in individual patients with inflammatory erosive arthritis.

This report covers the initial stages of work in the SSfM project Tools for Continuous Modelling and Simulation. The aims of the project are to improve the understanding and use of continuous modelling packages and to improve the confidence of model users in the quality of their results. The initial stages have investigated the application of sensitivity analysis, optimisation, and sampling methods to finite element models. The work has applied a variety of sensitivity analysis, optimisation and sampling methods to three small finite element models that cover a range of physical problems, complexities and interactions between model parameters. The aim of the work was to identify methods that repetably give accurate results with minimal computational eort, and to provide advice on algorithm selection Due to the varying nature of the test problems, this initial stage of work produced both model specific and more general conclusions that will be applied to two larger case studies in the next stage of the project.