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Utilising a Bayesian Combination M odel to Enhance G amma-ray Detection Precision

Utilising a Bayesian Combination M odel to Enhance G amma-ray Detection Precision. Andrew Parker Lancaster University Engineering Department. Borderline Waste – A Management Problem.

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Utilising a Bayesian Combination M odel to Enhance G amma-ray Detection Precision

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  1. Utilising a Bayesian Combination Model to Enhance Gamma-ray Detection Precision Andrew Parker Lancaster University Engineering Department

  2. Borderline Waste – A Management Problem “...where wastes are borderline between disposal categories the higher standard should be adopted for characterisation purposes.” – Nuclear Decommissioning Authority Table 1: The disposal cost per-cubic-metre, taken from LLWR at Drigg and NDA budget information Andrew Parker, Lancaster University Engineering Dept, 2011

  3. Gamma-ray Detectors LLW: Waste that has activity ... less than 12 GBq per tonne of gamma radioactivity Sodium Iodide Scintillator NaI Hyper-pure Germanium Semiconductor HPGe • Good energy resolution • Insensitive to temperature change • Poor detection efficiency relative to NaI. • High detection efficiency • Cheap to produce • Poor energy resolution Andrew Parker, Lancaster University Engineering Dept, 2011

  4. Bayesian Normal-Normal Model Bayes’ Rule Likelihood Posterior Value Prior Assuming the detectors’ results are normally distributed with Means and Standard Deviations (M, τ) & (Y,σ) respectively. Posterior Mean Posterior Variance Andrew Parker, Lancaster University Engineering Dept, 2011

  5. Combination of Count Data Table 2: Mean and standard deviation of Cs counts with the two detectors Levenberg-Marquardt fitting method applied to photopeaks. Example of Cs137 photopeak Table 3: Shows the Bayesian mean and standard deviation for the selected isotopes, having used all 15 result sets from each detector Andrew Parker, Lancaster University Engineering Dept, 2011

  6. Precision Comparison Results Coefficient of Variation (CV) Table 4: CV for single detector results Table 5: CV for the Bayesian method with varying values of N1 & N2 Where N1 = Number of sets of data used from Sodium Iodide (NaI) N2 = Number of sets of data used from Hyper-pure Germanium (HPGe) Andrew Parker, Lancaster University Engineering Dept, 2011

  7. Visual Comparison Bayesian Method HPGe NaI Figure 2: Plot showing the distributions of each detector alone and the plot of the Bayesian method using all available results for Cs 137. Normalised to zero.

  8. Conclusions • Under certain conditions the method has shown to reduce the normal distribution dispersion and therefore the precision of the result. • By obtaining a higher degree of precision the technique offers lower uncertainty when determining an accurate estimate for the activity of a source. • When fewer results were used the model shows higher levels of dispersion compared to that of a single detector. Thank you for listening, any questions related to the work? Andrew Parker (A.Parker4@Lancaster.ac.uk) Andrew Parker, Lancaster University Engineering Dept, 2011

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