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Title: An application of square root transformation for optimal prior selection Authors:  Cristiano Villa - Newcastle University (United Kingdom) [presenting]
Stephen Walker - University of Texas at Austin (United States)
Alfred Kume - University of Kent (United Kingdom)
Abstract: The pooling of opinions is a big area of research and has been for a number of decades. The idea is to obtain a single belief probability distribution from a set of expert opinion belief distributions. A new way is provided to provide a resultant prior opinion based on the optimal information among all possible linear combinations of the prior densities, including negative components. This is done in the square-root density space which is identified with the positive orthant of the Hilbert unit sphere of differentiable functions. It can be shown that the optimal prior is easily identified as an extrinsic mean in the sphere. For distributions belonging to the exponential family, the resulting calculations do not require numerical integration and can be immediately implemented in the Bayesian analysis. The idea can also be adopted for any neighbourhood of a chosen base prior and spanned by a finite set of ``contaminating'' directions.