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- W2567642012 abstract "Invariance properties of probability distributions have long been an area of interest in statistics and probability. In particular, much has been written about the famous de Finetti's theorem for infinitely exchangeable sequences and the Aldous-Hoover representation for infinitely exchangeable arrays. The key to both of these results is the existence of an infinite sequence or an infinite array. When this assumption fails, so do the aforementioned representation theorems. In this article we demonstrate this failure for the Aldous-Hoover representation and then develop a characterization theorem for the space of distributions that are invariant under a general finite group G. In particular, the results of Diaconis (1977) for finitely exchangeable sequences are a special case of our general result. We find sharp bounds on the total variation distance between distributions of finitely and infinitely partially exchangeable sequences and finitely and infinitely exchangeable arrays. Additionally we provide an example of the applicability of the theory for groups other than the symmetric group." @default.
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- W2567642012 date "2014-07-23" @default.
- W2567642012 modified "2023-09-27" @default.
- W2567642012 title "Characterization of Finite Group Invariant Distributions" @default.
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