Putting safeguards for BB full

[davidwalter2]

In the case for BB full with explicit parameters it previously could have happened that the beta parameter became negative. This happened when the nbeta parameter (the effective number of expected events after scaling with the betas) was below a certain threshold. To avoid this, the new parameter to be determined isu and defined as x = threshold + exp(u) ensuring x is always larger as the threshold and all beta parameters are always positive.

[bendavid]

Since this can't be used with a fully quadratic likelihood anyways, wouldn't it be more appropriate to have multiplicative BBB uncertainties in this case?

[davidwalter2]

Since this can't be used with a fully quadratic likelihood anyways, wouldn't it be more appropriate to have multiplicative BBB uncertainties in this case?

The BBB uncertainties are multiplicative. This is about finding the $x = \sum_j^{procs} n_j \beta_j$ per bin, which decouples the equations for the individual $\beta_j$ parameters. Ones we find $x$ we can compute $\beta_j$ analytically. But to find the $x$ we have to use 1D Newton minimization. To ensure it's above a certain threshold I've parameterized it as $x = threshold + \mathrm{e}^u$ such that I don't have to put any bound on $u$.

[bendavid]

Yes sorry I meant gamma or log-normal multiplicative.

But ok does this protection still preserve the mathematical properties that this is the proper minimum?