Bayesian inference about outputs of computationally expensive algorithms with uncertainty on the inputs
Haylock, Richard George Edward (1997) Bayesian inference about outputs of computationally expensive algorithms with uncertainty on the inputs. PhD thesis, University of Nottingham.
In the field of radiation protection, complex computationally expensive algorithms are used to predict radiation doses, to organs in the human body from exposure to internally deposited radionuclides. These algorithms contain many inputs, the true values of which are uncertain. Current methods for assessing the effects of the input uncertainties on the output of the algorithms are based on Monte Carlo analyses, i.e. sampling from subjective prior distributions that represent the uncertainty on each input, evaluating the output of the model and calculating sample statistics. For complex computationally expensive algorithms, it is often not possible to get a large enough sample for a meaningful uncertainty analysis. This thesis presents an alternative general theory for uncertainty analysis, based on the use of stochastic process models, in a Bayesian context. The measures provided by the Monte Carlo analysis are obtained, plus extra more informative measures, but using a far smaller sample. The theory is initially developed in a general form and then specifically for algorithms with inputs whose uncertainty can be characterised by independent normal distributions.
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