The equivalence between "domination of a bayesian experiment" and "a.e. domination of a statistical structure": the role of the predictive probability
Given a statistical structure 2 X, A, {Pθ : θ ∈ L}) and a probability measure µ on the parameter space (L, C), we consider a bayesian experiment (X × L, A ⊗ C, π). We concentrate our attention on the definitions of µ-a.e. dominated statistical structure and of dominated bayesian experiment. Under th...
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
1995-06-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1995(3)/381-389.pdf |
| _version_ | 1797817210586005504 |
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| author | C. MACCI |
| author_facet | C. MACCI |
| author_sort | C. MACCI |
| collection | DOAJ |
| description | Given a statistical structure 2 X, A, {Pθ : θ ∈ L}) and a probability measure µ on the parameter space (L, C), we consider a bayesian experiment (X × L, A ⊗ C, π). We concentrate our attention on the definitions of µ-a.e. dominated statistical structure and of dominated bayesian experiment. Under the assumption that A is countably generated, we prove that µ-a.e. domination of (X, A, {Pθ : θ ∈ L}) is equivalent to domination of (X × L, A ⊗ C, π). Furthermore, when (X, A, {Pθ : θ ∈ L}) is µ-a.e. dominated, the predictive probability is shown to be a possible µ-a.e. dominating measure.
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| first_indexed | 2024-03-13T08:50:32Z |
| format | Article |
| id | doaj.art-c8af39d59f294507b1165b850508c4e3 |
| institution | Directory Open Access Journal |
| issn | 1120-7183 2532-3350 |
| language | English |
| last_indexed | 2024-03-13T08:50:32Z |
| publishDate | 1995-06-01 |
| publisher | Sapienza Università Editrice |
| record_format | Article |
| series | Rendiconti di Matematica e delle Sue Applicazioni |
| spelling | doaj.art-c8af39d59f294507b1165b850508c4e32023-05-29T14:34:01ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33501995-06-01153381389The equivalence between "domination of a bayesian experiment" and "a.e. domination of a statistical structure": the role of the predictive probabilityC. MACCI Given a statistical structure 2 X, A, {Pθ : θ ∈ L}) and a probability measure µ on the parameter space (L, C), we consider a bayesian experiment (X × L, A ⊗ C, π). We concentrate our attention on the definitions of µ-a.e. dominated statistical structure and of dominated bayesian experiment. Under the assumption that A is countably generated, we prove that µ-a.e. domination of (X, A, {Pθ : θ ∈ L}) is equivalent to domination of (X × L, A ⊗ C, π). Furthermore, when (X, A, {Pθ : θ ∈ L}) is µ-a.e. dominated, the predictive probability is shown to be a possible µ-a.e. dominating measure. https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1995(3)/381-389.pdfstatistical structuresbayesian experimentsdominationpredictive probability |
| spellingShingle | C. MACCI The equivalence between "domination of a bayesian experiment" and "a.e. domination of a statistical structure": the role of the predictive probability Rendiconti di Matematica e delle Sue Applicazioni statistical structures bayesian experiments domination predictive probability |
| title | The equivalence between "domination of a bayesian experiment" and "a.e. domination of a statistical structure": the role of the predictive probability |
| title_full | The equivalence between "domination of a bayesian experiment" and "a.e. domination of a statistical structure": the role of the predictive probability |
| title_fullStr | The equivalence between "domination of a bayesian experiment" and "a.e. domination of a statistical structure": the role of the predictive probability |
| title_full_unstemmed | The equivalence between "domination of a bayesian experiment" and "a.e. domination of a statistical structure": the role of the predictive probability |
| title_short | The equivalence between "domination of a bayesian experiment" and "a.e. domination of a statistical structure": the role of the predictive probability |
| title_sort | equivalence between domination of a bayesian experiment and a e domination of a statistical structure the role of the predictive probability |
| topic | statistical structures bayesian experiments domination predictive probability |
| url | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1995(3)/381-389.pdf |
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