ENBIS-16 in Sheffield

11 – 15 September 2016; Sheffield Abstract submission: 20 March – 4 July 2016

Prior Information, but no MCMC: A Bayesian Normal Linear Regression Case Study

12 September 2016, 11:50 – 12:10


Submitted by
Katy Klauenberg
Katy Klauenberg (Physikalisch-Technische Bundesanstalt), Gerd Wübbeler (Physikalisch-Technische Bundesanstalt), Bodo Mickan (Physikalisch-Technische Bundesanstalt), Peter Harris (National Physical Laboratory), Clemens Elster (Physikalisch-Technische Bundesanstalt)
Regression is a very common task and frequently additional a priori information exists. Bayesian inference is well suited for these situations. However, often the need for MCMC methods and difficulties in eliciting prior distributions prevent the application of Bayesian inference.

Oftentimes prior knowledge is available from an ensemble of previous, similar regressions. Pooling the posterior distributions from previous regressions and approximating the average by a wide distribution from a parametric family is suitable to describe practitioners' a priori belief of a similar regression. Likewise for linear regression models with Gaussian measurement errors: prior information from previous regressions can often be expressed by the normal inverse Gamma distribution - a conjugate prior. Yielding an analytical, closed form posterior distribution, one can easily derive estimates, uncertainties and credible intervals for all parameters, the regression curve as well as predictions for this class of problems. In addition, we describe Bayesian tools to assess the plausibility of assumptions behind the suggested approach - also without Markov Chain Monte Carlo (MCMC) methods.

A typical problem from metrology will demonstrate the practical value. We apply the Normal linear regression with conjugate priors to the calibration of a flow device and illustrate how prior knowledge from previous calibrations may enable robust predictions even for extrapolations. In addition we provide software and suggest graphical displays to also enable practitioners to apply Bayesian Normal linear regression.

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