Estimation across multiple models with application to Bayesian computing and software development |
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Authors: | Richard J Stevens Trevor J Sweeting |
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Institution: | (1) Cancer Epidemiology Unit, Richard Doll Building, Old Road Campus, Roosevelt Drive, Oxford, OX3 7LF, UK;(2) Department of Statistical Science, University College London, London, UK |
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Abstract: | Statistical models are sometimes incorporated into computer software for making predictions about future observations. When
the computer model consists of a single statistical model this corresponds to estimation of a function of the model parameters.
This paper is concerned with the case that the computer model implements multiple, individually-estimated statistical sub-models.
This case frequently arises, for example, in models for medical decision making that derive parameter information from multiple
clinical studies. We develop a method for calculating the posterior mean of a function of the parameter vectors of multiple
statistical models that is easy to implement in computer software, has high asymptotic accuracy, and has a computational cost
linear in the total number of model parameters. The formula is then used to derive a general result about posterior estimation
across multiple models. The utility of the results is illustrated by application to clinical software that estimates the risk
of fatal coronary disease in people with diabetes. |
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Keywords: | Bayesian inference Asymptotic theory Computer models |
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