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Suppose an app's user specifies several Normal priors by setting the mean and variance for each. I'd like to display a combined plot with the prior pdfs, like that on the figure. enter image description here.

Q: What is a good way to compute the plot bounds for reasonable visualisation?

I've considered alternatives, eg:

  • set the smallest $(\mu_i - 3\sigma_i)$ and largest $(\mu_i - 3\sigma_ i)$ for the left and right bound, respectively. (Here, $i$ indexes the priors.)
  • set the bounds using a small threshold for the derivative of each $pdf_i$.

The difficulty is caused by possibly disparate priors: flat vs sharp. There are UI solutions (e.g. user-defined plot bounds) but they're laborious, and ignore the initial bounds choice for display initialisation.

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