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For an exponential model with scalar parameter, WelchP:1963 examined the role of Bayesian analysis in statistical inference, more specifically the use of the Jeffreys:1946 prior. They determined that Bayesian intervals and thus in effect Bayesian quantiles had second order confidence accuracy. We use a Taylor series expansion of the log-model to develop a second order version of the vector exponential model; this is developed as a contribution to theory in statistics at a time when algorithms are prominent, and it provides a basis for generalizing the Welch-Peers approach to the vector parameter context.
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