Module poisson 

Poisson-likelihood optimizer for low-count neutron data.

When neutron counts are low (< ~30 per bin), the Gaussian/chi-squared assumption breaks down and Poisson statistics must be used directly.

Negative log-likelihood

L(θ) = Σᵢ [y_model(θ)ᵢ - y_obs,ᵢ · ln(y_model(θ)ᵢ)]

This is minimized using a projected optimizer:

• damped Gauss-Newton / Fisher steps when an analytical Jacobian exists
• finite-difference projected gradient fallback otherwise

Both paths use backtracking line search and bound constraints (non-negativity on densities).

TRINIDI Reference

• trinidi/reconstruct.py — Poisson NLL and APGM optimizer

Structs

CountsBackgroundScaleModel

Counts model with optional nuisance scaling of signal and detector background.

CountsModel

Convert transmission model + counts to a counts-based forward model.

PoissonConfig

Configuration for the Poisson optimizer.

PoissonResult

Result of Poisson-likelihood optimization.

TransmissionKLBackgroundModel

KL-compatible background model for transmission data.

Functions

poisson_fit

Run Poisson-likelihood optimization using a projected KL optimizer.