Say a domain expert comes up to us and ask to the of his . He actually knows the and needs uncertainty bounds on his parameters. How would we do that?

More explanation: For many of our problems, we get to choose our model. In classifying cats from dogs, we get to choose between neural nets and SVMs. In finding clusters, we get to choose between K-means or PCA. Now what if a domain expert has an model, but needs to find the parameters.

Example: Let’s say the known model is

y(x) = exp(-a*x) + b*x + sin(c*x) + d

  • where sample points x_i ~ Uniform(0, 1) and

  • observations y_{i} ~ y(x_i) + Normal(0, variance)

Here are some images: examples

and here is the for generating these images

TL;DR How to find confidence bounds on a, b, c, and d?

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