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- W2264402012 abstract "A length-$n$ random sequence $X_1,ldots,X_n$ in a space $S$ is finitely exchangeable if its distribution is invariant under all $n!$ permutations of coordinates. Given $N > n$, we study the extendibility problem: when is it the case that there is a length-$N$ exchangeable random sequence $Y_1,ldots, Y_N$ so that $(Y_1,ldots,Y_n)$ has the same distribution as $(X_1,ldots,X_n)$? In this paper, we give a necessary and sufficient condition so that, for given $n$ and $N$, the extendibility problem admits a solution. This is done by employing functional-analytic and measure-theoretic arguments that take into account the symmetry. We also address the problem of infinite extendibility. Our results are valid when $X_1$ has a regular distribution in a locally compact Hausdorff space $S$. We also revisit the problem of representation of the distribution of a finitely exchangeable sequence." @default.
- W2264402012 created "2016-06-24" @default.
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- W2264402012 date "2015-01-25" @default.
- W2264402012 modified "2023-09-24" @default.
- W2264402012 title "On the extendibility of finitely exchangeable probability measures" @default.
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- W2264402012 doi "https://doi.org/10.48550/arxiv.1501.06188" @default.
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