Simulating the component counts of combinatorial structures
| Autor: | Andrew Barbour, Richard Arratia, Warren J. Ewens, Simon Tavaré |
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| Přispěvatelé: | Apollo - University of Cambridge Repository, University of Zurich, Tavaré, Simon |
| Rok vydání: | 2018 |
| Předmět: |
0301 basic medicine
Logarithm Evolution Structure (category theory) Asymptotic distribution 01 natural sciences 010104 statistics & probability 03 medical and health sciences 510 Mathematics Behavior and Systematics Spaghetti loop distribution Component (UML) Applied mathematics Computer Simulation Poisson Distribution 0101 mathematics Ecology Evolution Behavior and Systematics Mathematics Probability Random mappings Models Statistical Ecology Random permutations 1. No poverty Ewens sampling formula Coupling (probability) 10123 Institute of Mathematics 030104 developmental biology Distribution (mathematics) 1105 Ecology Evolution Behavior and Systematics Logistic Models Feller coupling Chinese restaurant process Random variable Algorithms |
| Popis: | This article describes and compares methods for simulating the component counts of random logarithmic combinatorial structures such as permutations and mappings. We exploit the Feller coupling for simulating permutations to provide a very fast method for simulating logarithmic assemblies more generally. For logarithmic multisets and selections, this approach is replaced by an acceptance/rejection method based on a particular conditioning relationship that represents the distribution of the combinatorial structure as that of independent random variables conditioned on a weighted sum. We show how to improve its acceptance rate. We illustrate the method by estimating the probability that a random mapping has no repeated component sizes, and establish the asymptotic distribution of the difference between the number of components and the number of distinct component sizes for a very general class of logarithmic structures. |
| Databáze: | OpenAIRE |
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