Linearity check about bayem HOT 3 OPEN

I am not sure if I could fully understand all challenges you mentioned. Only some thoughts of mine:

1. First a general thing that I am not 100% sure about, but as far as I learnt in a recent course at the Uni, a sampling procedure is valid as long as NO significant correlation among samples of unknown parameters exists. This requirement is, however, violated in the above example if I see it correctly. The samples of parameters E_beam and E_conn are quite highly correlated !

2. I think, the question of how good/bad a function is linearized around a specific point can be answered based on the second derivative of that function. Reason: the accuracy level of a linearization directly goes to that of a Taylor expansion which has been truncated from the second derivative onward, e.g. if the second derivative of a function is quite high, a linearization introduces quite too much inaccuracy. So, IMO, a logical approach is to find a good indicator for how large the second derivative is. For that purpose, we can compare the first derivative at "an appropriate set of different points in the neighborhood of the mean point". Now the question is, what would be "an appropriate set of different points in the neighborhood of the mean point" in a high-dimensional space of parameters ? ... hmm ... interesting to think about it.

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You could try to compute the diagonal entries of the second derivates (so for a single parameter) at the MAP and try to estimate the error resulting from that onto the posterior (sum_i dTheta_post_mean/dH2 * dH2) und analog dTheta_post_std/dH2 * dH2.

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#90 Tries to provide a solution.

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