A Bayesian approach to estimate ambient dose equivalent for liquid radioactive waste measurements

To support regulatory clearance decisions for liquid radioactive waste (LRW) under in-situ constraints, ambient dose equivalent assessment must be reliable with limited acquisition time while minimizing occupational exposure. This study proposes a Bayesian Weighted Least Squares (B-WLS) framework to derive a spectrum-to-dose conversion operator, G(E), that infers H^∗(10) directly from short-count gamma-ray spectra. A 1-inch LaBr₃(Ce) scintillation detector was implemented, and a detector response matrix was constructed using an MCNP6 model calibrated with Gaussian energy broadening to match measured resolution. The G(E) function was parameterized as a polynomial in log₁₀(E) and its coefficients were estimated using three approaches: least squares method (LSM), adaptive moment estimation (Adam) optimizer, and the proposed B-WLS method with heteroscedastic weighting and Bayesian regularization. The performance was validated using ¹³⁷Cs and ⁶⁰Co spectra acquired at multiple dose rate levels and compared against theoretical dose rates. A model-order sensitivity analysis identified distinct optimal polynomial orders, with B-WLS achieving the lowest mean absolute percentage error (MAPE) of 1.17% among the evaluated methods. Across dose rate conditions, B-WLS showed the most consistent linearity and reduced sensitivity to low-count fluctuations, providing stable inference in low-dose regimes where the deterministic methods are more vulnerable to channel-level statistical variability. These results indicate that Bayesian regression with heteroscedastic weighting offers an operationally robust option for field-deployable G(E)-based dose rate screening of LRW, supporting conservative decision-making in radiation protection.