Using Test Plans for Bayesian Modeling

When modeling technical processes, the training data regularly come from test plans, to reduce the number of experiments and to save time and costs. On the other hand, this leads to unobserved combinations of the input variables. In this article it is shown, that these unobserved configurations might lead to un-trainable parameters. Afterwards a possible design criterion is introduced, which avoids this drawback. Our approach is tested to model a welding process. The results show, that hybrid Bayesian networks are able to deal with yet unobserved in- and output data.

[1]  Kevin P. Murphy,et al.  A Variational Approximation for Bayesian Networks with Discrete and Continuous Latent Variables , 1999, UAI.

[2]  Uri Lerner,et al.  Exact Inference in Networks with Discrete Children of Continuous Parents , 2001, UAI.

[3]  Steffen L. Lauritzen,et al.  Stable local computation with conditional Gaussian distributions , 2001, Stat. Comput..

[4]  Jim Rutledge.  An Introduction to Design of Experiments: A Simplified Approach , 2000, Technometrics.

[5]  Kevin P. Murphy,et al.  Inference and Learning in Hybrid Bayesian Networks , 1998 .

[6]  Joachim Denzler,et al.  Non-linear modeling of a production process by hybrid Bayesian Networks 1 , 2005 .

[7]  S. Lauritzen.  Propagation of Probabilities, Means, and Variances in Mixed Graphical Association Models , 1992 .

[8]  Kristian G. Olesen,et al.  Causal Probabilistic Networks with Both Discrete and Continuous Variables , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[10]  Kevin Murphy,et al.  Bayes net toolbox for Matlab , 1999 .

[11]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[12]  Robert Cowell,et al.  Advanced Inference in Bayesian Networks , 1999, Learning in Graphical Models.

[13]  P. Hein,et al.  Manufacturing system for the integrated hydroforming, trimming and welding of sheet metal pairs , 2001 .

[14]  Michael I. Jordan.  Learning in Graphical Models , 1999, NATO ASI Series.

[15]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.