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Pooling information from multiple, independent studies (meta-analysis) adds great value to medical research. Random effects models are widely used for this purpose. However, there are many different ways of estimating model parameters, and the choice of estimation procedure may be influential upon the conclusions of the meta-analysis. In this paper, we describe a recently proposed Bayesian estimation procedure and compare it with a profile likelihood method and with the DerSimonian-Laird and Mandel-Paule estimators including the Knapp-Hartung correction. The Bayesian procedure uses a non-informative prior for the overall mean and the between-study standard deviation that is determined by the Berger and Bernardo reference prior principle. The comparison of these procedures focuses on the frequentist properties of interval estimates for the overall mean. The results of our simulation study reveal that the Bayesian approach is a promising alternative producing more accurate interval estimates than those three conventional procedures for meta-analysis. The Bayesian procedure is also illustrated using three examples of meta-analysis involving real data. Copyright © 2016 John Wiley & Sons, Ltd.

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Evaluation of measurement uncertainty is considered when the value of the measurand depends on the continuous variable time. A concept of dynamic measurement uncertainty is introduced by generalizing the GUM approach. The concept is applied to linear and time-invariant systems which are often appropriate to model dynamic measurements. Digital filtering is proposed for estimating the time-dependent value of the measurand and the design of an appropriate FIR filter is described. Dynamic uncertainty evaluation is then carried out for this analysis and conditions are specified for its proper use. The approach is illustrated for the particular example of a second-order model. It is shown in terms of simulations that the proposed analysis yields significantly improved results when compared with the sometimes applied quasi-static treatment.

The task of analysing dynamic measurements is considered for the case that the input–output behaviour of the employed sensor can be described in terms of a second-order dynamic model. It is assumed that estimates of the parameters of this model are available which have been determined by the analysis of previous dynamic calibration measurements. The goal is to estimate the unknown input of the sensor given its discrete-time output signal. It is proposed to apply an FIR filter which is constructed according to the underlying dynamic model. The uncertainties associated with the obtained estimates of the time-dependent measurand are then determined by taking into account the uncertainty associated with the estimates of the parameters of the dynamic model, the uncertainty of the sensor's output signal and the applied signal processing steps. The proposed procedure allows real-time calculations including the real-time calculation of uncertainties, and it could therefore be directly integrated into the measurement chain. Utilizing dynamic calibration measurements of accelerometers, the proposed analysis is demonstrated by its application to acceleration measurements upon shock excitations.