Normal‑inverse‑gamma (NIG) regression is not uniquely identifiable from its marginal Student‑t likelihood: the likelihood fixes three combinations of the four NIG parameters, leaving a one‑dimensional fiber of indistinguishable solutions. We resolve this fiber by incorporating an independent physical measurement.
In an initial embodiment, a reconstruction network receives a single noisy filtered‑backprojection (FBP) image and is first trained solely with the Student‑t negative log‑likelihood to estimate the three identifiable coordinates $(\gamma, \alpha, c)$. The network is then frozen; repeated physical‑noise realizations propagated through its output generate a Monte Carlo (MC) teacher label for the output‑domain aleatoric variance. An aleatoric head attached to the frozen features learns this label, after which the remaining parameters $(\beta, \nu)$ are recovered algebraically.
On 30 held‑out simulated objects at five photon levels, one‑image predictions achieved pooled Spearman correlations of 0.832‑0.951 against independent 400‑repeat references, median within‑image correlations of 0.834‑0.947, and 98.81‑99.55% of evaluated pixels satisfied the algebraic admissibility condition. The method requires no KL term, reference prior, evidence regularizer, or cross‑loss weight.
Review