Tanaka and Komaki (Sankhya Ser A Indian Stat Inst 73-A:162–184, 2011) proposed superharmonic priors in Bayesian time series analysis as alternative to the famous Jeffreys prior. By definition the existence of superharmonic priors on a specific time series model with finite-dimensional parameter is equivalent to that of positive nonconstant superharmonic functions on the corresponding Riemannian manifold endowed with the Fisher metric. In the autoregressive models, whose Fisher metric and its inverse have quite messy forms, we obtain superharmonic priors in an explicit manner To derive this result, we developed a systematic way of dealing with symmetric polynomials, which are related to Schur functions.

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• Superharmonic priors for autoregressive models