Bayesian methods are a powerful tool when making decisions in the presence of uncertainty. Not only do they provide a mathematical framework of incorporating information from both theoretical and experimental sources, but they also quantify the value that can be gained from additional information, such as further experimentation. Consequently, experimental design can be optimized directly in terms of the value added. Manufacturing decisions can often depend on complex functions. In this work, Bayesian methods for predicting functions are explored. First, Brownian distributions, a relatively simple class of distributions with some useful properties are introduced. To illustrate how Brownian distributions can be used in a manufacturing situation, experimental design for stability limit prediction is treated in a case study. In addition, a method of building general distributions from underlying dynamical models is introduced.

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