Finite Exchangeable Sequences

By Persi Diaconis, David Freedman. 1980

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Deep Factors for Forecasting (2019, methodology): “It follows from de Finetti’s theorem (Diaconis, 1977; Diaconis & Freedman, 1980) that Since z i are time series, we can decompose p ( z i | g ) in the causal direction using the chain rule as Substituting this into the de Finetti factorization in Eqn.”
The Theory of Quantum Information (2018, result): “A finite quantum formulation of de Finetti’s theorem, closer in spirit to classical results due to Diaconis and Freedman [59], was proved by König and Renner [133].”
q-exchangeability via quasi-invariance (2009, background): “equence of large-nproperties of the binomial coefﬁcients that enter the multivariate hypergeometric distribution in the model of random sampling without replacement, inherent to the action of Sn. See [DF] for quantitative aspects of the relation between ﬁnite and inﬁnite exchangeability. Alternative”
Logarithmic Combinatorial Structures: A Probabilistic Approach (2003, methodology): “The quality of such approximations is assessed using metrics, including the total variation distance, by Stam (1978) and Diaconis and Freedman (1980).”
The distance correlation t-test of independence in high dimension (2013, background): “See also Diaconis and Freedman [5]. ii.”
Unknown Quantum States and Operations, a Bayesian View (2004, unknown): “In particular, we are thinking of such issues as representation theorems for finitely exchangeable distributions [52,75].”
Probability and Mathematical Genetics: More uses of exchangeability: representations of complex random structures (2009, background): “mit of ﬁnite objects, and in the “25 years ago” surveys such convergence ideas were explicit in the context of weak convergence for “sampling without replacement” processes, in ﬁnite versions such as [24], and in some other contexts, such as Kingman’s theory of exchangeable random partitions. I prev”
Probabilistic Symmetries and Invariant Neural Networks (2020, background): “…because it computes the probability of sampling any sequence without replacement from an urn with n balls, each labeled by an element of Xn. 15 Diaconis and Freedman (1980a) and Kallenberg (2005, Proposition 1.8) prove results (in different forms) similar to Theorem 11 that rely on the urn…”
Higher‐Dimensional Coulomb Gases and Renormalized Energy Functionals (2013, methodology): “a classical combinatorial trick that seems to go back to [Gru] and can be found e.g. in [HM, Proof of Lemma 8] or [Rou, Proof of Theorem 2.2]. In fact we are here using the de Finetti-type theorem of [DF] in disguise. Then, in view of the condition on q we have p > d and thus the Sobolev embeddin”
Symmetry of large physical systems implies independence of subsystems (2007, background): “De Finetti’s representation of symmetric states in terms of i.i.d. states is, however, inherently limited to the case where n ≪ N . the That is, given a large N -partite symmetric state, i.i.d. property generally only holds approximatively for a small n -partite subsystem [DF80] (see Fig.”
Subjective Probability: The Real Thing (2004, unknown): “, Xn ≤ tn) = ∫ ∞ 0 ∏n i=1 Φ(δti)dπ(δ) Ferguson, T. “Prior distributions on spaces of probability measures”, Ann. Stat. 2 (1974) 615–629 contains examples of the various attempts to choose such a prior.”
Derivation of Hartree's theory for generic mean-field Bose systems (2013, background): “This result is a quantum generalization of the famous classical de Finetti, also called Hewitt-Savage, theorem [14, 15, 19, 30, 18] about symmetric probability measures having an infinite number of variables.”