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Compute ceneter time of particle transit in laser beam (tao) using max likelihood#82

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jtgasparik wants to merge 8 commits intoARM-DOE:mainfrom
jtgasparik:tao_max_likelihood
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Compute ceneter time of particle transit in laser beam (tao) using max likelihood#82
jtgasparik wants to merge 8 commits intoARM-DOE:mainfrom
jtgasparik:tao_max_likelihood

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Estimate tau_hat using the Moteki & Kondo (2008) grid-search MLE.

This implements the normalized-derivative framework from the paper:
  - S'(t)/S(t) = I'(t)/I(t) + C_sca'(t)/C_sca(t)  [Eq. (4)]
  - For the Gaussian beam, I'(t)/I(t) = -(t - tau)/sigma^2  [Eq. (5)]
  - Likelihood of a p-point subset is multivariate normal [Eq. (A.9)]
  - Mean vector uses Eq. (A.4)
  - Covariance/variance use Eqs. (A.10a), (A.10b)
  - Signal-noise model uses Eq. (A.6)
  - Error propagation to the derivative uses Eq. (A.7)
  - tau is found by grid search over a 1D parameter space [Appendix A.5]

Computed values are tested for non-evaporative particles (events 499 and 1040).

@jtgasparik jtgasparik requested a review from rcjackson March 20, 2026 21:02
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