Academic literature on the topic 'Exchangeable probability partition function'

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Journal articles on the topic "Exchangeable probability partition function"

1

Bassetti, Federico, and Lucia Ladelli. "Mixture of Species Sampling Models." Mathematics 9, no. 23 (2021): 3127. http://dx.doi.org/10.3390/math9233127.

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We introduce mixtures of species sampling sequences (mSSS) and discuss how these sequences are related to various types of Bayesian models. As a particular case, we recover species sampling sequences with general (not necessarily diffuse) base measures. These models include some “spike-and-slab” non-parametric priors recently introduced to provide sparsity. Furthermore, we show how mSSS arise while considering hierarchical species sampling random probabilities (e.g., the hierarchical Dirichlet process). Extending previous results, we prove that mSSS are obtained by assigning the values of an e
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2

Kurt, Noemi, and Mathias Rafler. "Recursions for the exchangeable partition function of the seedbank coalescent." Theoretical Population Biology 114 (April 2017): 95–106. http://dx.doi.org/10.1016/j.tpb.2016.12.002.

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3

Crane, Harry, and Peter McCullagh. "Reversible Markov structures on divisible set partitions." Journal of Applied Probability 52, no. 03 (2015): 622–35. http://dx.doi.org/10.1017/s0021900200113336.

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We studyk-divisible partition structures, which are families of random set partitions whose block sizes are divisible by an integerk= 1, 2, …. In this setting, exchangeability corresponds to the usual invariance under relabeling by arbitrary permutations; however, fork> 1, the ordinary deletion maps on partitions no longer preserve divisibility, and so a random deletion procedure is needed to obtain a partition structure. We describe explicit Chinese restaurant-type seating rules for generating families of exchangeablek-divisible partitions that are consistent under random deletion. We
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4

Speed, T. P., and H. L. Silcock. "Cumulants and partition lattices VI. variances and covariances of mean squares." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 44, no. 3 (1988): 362–88. http://dx.doi.org/10.1017/s1446788700032158.

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AbstractFormulae are given for the variances and covariances for mean squares in anova under the broadest possible assumptions. The results of ther authors are obtained by specializing appropriately: these include ones concerning randomization and/or random sampling models, as well as additive (linear) models consisting of mutually independent sets of exchangeable effects. Although the illustrations given refer only to doubly and triply-indexed arrays, the approach is quite general. Particular attention is drawn to the generalized cumulants (and their natural unbiased estimators) which vanish
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5

GNEDIN, ALEXANDER, and JIM PITMAN. "Poisson Representation of a Ewens Fragmentation Process." Combinatorics, Probability and Computing 16, no. 6 (2007): 819–27. http://dx.doi.org/10.1017/s0963548306008352.

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A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of [n] = 1,. . .,nat time θ ≥ 0 is governed by the Ewens sampling formula with parameter θ. These partition-valued processes are exchangeable and consistent, asnvaries. They can be derived by uniform sampling from a corresponding mass fragmentation process defined by cutting a unit interval at the points of a Poisson process with intensity θx−1dx on/mathbbR+, arranged to beintensifying as θ increases.
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6

Ono, Ken. "Distribution of the Partition Function Modulo m." Annals of Mathematics 151, no. 1 (2000): 293. http://dx.doi.org/10.2307/121118.

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7

de Tilière, Béeatrice. "Partition function of periodic isoradial dimer models." Probability Theory and Related Fields 138, no. 3-4 (2006): 451–62. http://dx.doi.org/10.1007/s00440-006-0041-2.

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8

Watson, G. S. "An ordering inequality for exchangeable random variables." Advances in Applied Probability 18, no. 1 (1986): 274–76. http://dx.doi.org/10.2307/1427246.

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Let X1, · ··, Xn be exchangeable random variables with finite variance and two sequences of constants satisfying a1≦···≦an, b1≦···≦bn. Suppose that a′1, ···, a′n is a rearrangement of a1, ···, an and that g(x) is a non-decreasing function. Then
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9

Hansen, Jennie C. "A functional central limit theorem for the Ewens sampling formula." Journal of Applied Probability 27, no. 1 (1990): 28–43. http://dx.doi.org/10.2307/3214593.

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For each n > 0, the Ewens sampling formula from population genetics is a measure on the set of all partitions of the integer n. To determine the limiting distributions for the part sizes of a partition with respect to the measures given by this formula, we associate to each partition a step function on [0, 1]. Each jump in the function equals the number of parts in the partition of a certain size. We normalize these functions and show that the induced measures on D[0, 1] converge to Wiener measure. This result complements Kingman's frequency limit theorem [10] for the Ewens partition struct
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10

Hoyle, David C. "Replica analysis of the lattice-gas restricted Boltzmann machine partition function." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 1 (2023): 013301. http://dx.doi.org/10.1088/1742-5468/acaf83.

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Abstract We study the expectation value of the logarithm of the partition function of large binary-to-binary lattice-gas restricted Boltzmann machines (RBMs) within a replica-symmetric ansatz, averaging over the disorder represented by the parameters of the RBM Hamiltonian. Averaging over the Hamiltonian parameters is done with a diagonal covariance matrix. Due to the diagonal form of the parameter covariance matrix not being preserved under the isomorphism between the Ising and lattice-gas forms of the RBM, we find differences in the behaviour of the quenched log partition function of the lat
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