# Probabilistic risk bounds for the characterization of radiological contamination

## TL;DR

This paper introduces new probabilistic methods for estimating risk bounds in radiological contamination characterization, especially effective with small sample sizes and weak distributional assumptions.

## Contribution

It proposes alternative statistical approaches based on probabilistic inequalities and order-statistics, avoiding strong Gaussian assumptions for risk estimation.

## Key findings

- Methods validated on synthetic data with known distributions.
- Applied successfully to real radiological measurement data.
- Provided conservative probabilistic risk bounds with limited data.

## Abstract

The radiological characterization of contaminated elements (walls, grounds, objects) from nuclear facilities often suffers from a too small number of measurements. In order to determine risk prediction bounds on the level of contamination, some classic statistical methods may then reveal unsuited as they rely upon strong assumptions (e.g. that the underlying distribution is Gaussian) which cannot be checked. Considering that a set of measurements or their average value arise from a Gaussian distribution can sometimes lead to erroneous conclusion, possibly underconservative. This paper presents several alternative statistical approaches which are based on much weaker hypotheses than Gaussianity. They result from general probabilistic inequalities and order-statistics based formula. Given a data sample, these inequalities make it possible to derive prediction intervals for a random variable, which can be directly interpreted as probabilistic risk bounds. For the sake of validation, they are first applied to synthetic data samples generated from several known theoretical distributions. In a second time, the proposed methods are applied to two data sets obtained from real radiological contamination measurements.