Exchangeability of observations corresponds to a condition shared by the vast majority of applications of the Bayesian paradigm. By de Finetti's representation theorem, if exchangeable observations form an infinite sequence of random variables, then they are conditionally independent and identically distributed given some random parameter, which is the main object of statistical inference. Such parameter is a limiting mathematical entity and therefore hypotheses related to it might be not verifiable. For this reason, statistical analysis should be directed toward the prevision of the empirical distribution of N observations. In view of these considerations, two specific forms of (finitary) exchangeable laws are introduced and studied: one is based on sequences of nested partitions and the other one rests on the concept of exchangeable random partition.

(2007). Statistical issues connected with finitary exchangeable sequences. (Tesi di dottorato, Università degli Studi di Pavia, 2007).

### Statistical issues connected with finitary exchangeable sequences

#### Abstract

Exchangeability of observations corresponds to a condition shared by the vast majority of applications of the Bayesian paradigm. By de Finetti's representation theorem, if exchangeable observations form an infinite sequence of random variables, then they are conditionally independent and identically distributed given some random parameter, which is the main object of statistical inference. Such parameter is a limiting mathematical entity and therefore hypotheses related to it might be not verifiable. For this reason, statistical analysis should be directed toward the prevision of the empirical distribution of N observations. In view of these considerations, two specific forms of (finitary) exchangeable laws are introduced and studied: one is based on sequences of nested partitions and the other one rests on the concept of exchangeable random partition.
##### Scheda breve Scheda completa Scheda completa (DC) Regazzini, Eugenio
Bayesian statistic, finitary exchangeable sequences
English
19-gen-2007
Matematica e Statistica
19
2006/2007
Università degli Studi di Pavia
(2007). Statistical issues connected with finitary exchangeable sequences. (Tesi di dottorato, Università degli Studi di Pavia, 2007).
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Descrizione: Tesi di dottorato
Tipologia di allegato: Doctoral thesis
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/443781`
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