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dwelltime: add standard errors based on hessian approximation #690

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dwelltime: add standard errors based on hessian approximation #690

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Commits on Oct 29, 2024

  1. dwelltime: add asymptotic standard errors 

    When calculating the asymptotic uncertainty interval, we should take into account that we actually impose a linear sum constraint (otherwise, the amplitudes will have indeterminate confidence intervals).

One could add the constraint explicitly to the Hessian by simply adding a large penalty term to the relevant derivatives. Considering that the sum constraint is of the form (1 - sum(a_i)) ** 2, this would result in adding a constant term d^2f/daidaj = -c with c large to all amplitude terms.

What is ugly is that we would need to choose this constant as large as possible without incurring numerical issues. This is why it is preferable to project onto the null space and then calculate the result back instead.
    @JoepVanlier
    JoepVanlier committed Oct 29, 2024
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  2. profiles: provide the option to plot w/stderr

    @JoepVanlier
    JoepVanlier committed Oct 29, 2024
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