On a notion of partially conditionally identically distributed sequences
| Autor: | Sandra Fortini, Polina Sporysheva, Sonia Petrone |
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| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Independent and identically distributed random variables Pure mathematics PREDICTION 01 natural sciences Bayesian nonparametrics 010104 statistics & probability LIMIT THEOREMS Law of large numbers FOS: Mathematics REINFORCED PROCESSES Limit (mathematics) 0101 mathematics Mathematics Central limit theorem Applied Mathematics 010102 general mathematics PARTIAL EXCHANGEABILITY Probability (math.PR) Extension (predicate logic) Bayesian statistics EXCHANGEABILITY Modeling and Simulation SPREADABILITY Focus (optics) BAYESIAN NONPARAMETRICS Mathematics - Probability EXCHANGEABILITY PARTIAL EXCHANGEABILITY REINFORCED PROCESSES SPREADABILITY LIMIT THEOREMS PREDICTION BAYESIAN NONPARAMETRICS |
| DOI: | 10.48550/arxiv.1608.00471 |
| Popis: | A notion of conditionally identically distributed (c.i.d.) sequences has been studied as a form of stochastic dependence weaker than exchangeability, but equivalent to it in the presence of stationarity. We extend such notion to families of sequences. Paralleling the extension from exchangeability to partial exchangeability in the sense of de Finetti, we propose a notion of partially c.i.d. dependence, which is shown to be equivalent to partial exchangeability for stationary processes. Partially c.i.d. families of sequences preserve attractive limit properties of partial exchangeability, and are asymptotically partially exchangeable. Moreover, we provide strong laws of large numbers and two central limit theorems. Our focus is on the asymptotic agreement of predictions and empirical means, which lies at the foundations of Bayesian statistics. Natural examples of partially c.i.d. constructions are interacting randomly reinforced processes satisfying certain conditions on the reinforcement. |
| Databáze: | OpenAIRE |
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