Bayesian inference about a quantity is made through the probability density function that describes the state of incomplete knowledge acquired from measurement. This approach can be applied advantageously to evaluate the data obtained from repeated measurements of a quantity, with or without added information on the variances or error bounds of the indicated values. Results are compared with those obtained using conventional statistical theory. It is concluded that Bayesian inference allows a flexible and natural characterization of the measurement uncertainty.
Recent work referred to two approaches for doing a Bayesian analysis for simple linear calibration and pointed out that there could be a difference between the results of applying the procedure of GUM Supplement 1 and one of those approaches. It will be shown that the difference between the two Bayesian approaches reflects the use of two different priors. It will be shown that the results obtained by GUM Supplement 1 are those of a Bayesian analysis with commonly used priors and a measurement equation that satisfies the principles of the Guide to the Expression of Uncertainty in Measurement (GUM).
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