Three of the basic questions of Statistics may be stated as follows: (A) Which portion of the data X is actually informative about the parameter of interest (theta)? (B) How can all the relevant information about (theta) provided by the data X be extracted? (C) What kind of information about (theta) do the data X possess? / The perspective of this dissertation is that of a Bayesian. / Chapter I is essentially concerned with question A. The theory of conditional independence is explained and the relations between ancillarity, sufficiency, and statistical independence are discussed in depth. Some related concepts like specific sufficiency, bounded completeness, and splitting sets are also studied in some details. The language of conditional independence is used in the remaining Chapters. / Chapter II deals with question B for the particular problem of analysing categorical data with missing entries. It is demonstrated how a suitably chosen prior for the frequency parameters can streamline the analysis in the presence of missing entries due to non-response or other causes. The two cases where the data follow the Multinomial or the Multivariate Hypergeometric model are treated separately. In the first case it is adequate to restrict the prior (for the cell probabilities) to the class of Dirichlet distributions. In the Hypergeometric case it is convenient to select a prior (for the cell population frequencies) from the class of Dirichlet-Multinomial (DM) distributions. The DM distributions are studied in detail. / Chapter III is directly related to question C. Conditions on the likelihood function and on the prior distribution are presented in order to assess the effect of the sample on the posterior distribution. More specifically, it is shown that under certain conditions, the larger the observations obtained, the larger (stochastically in terms of the posterior distribution) is the appropriate parameter. / Finally, Chapter IV deals with the characterization of distributions in terms of Blackwell comparison of experiments. It is shown that a result (for the Hypergeometric model) obtained in Chapter II is actually a consequence of a property of complete families of distributions. / Source: Dissertation Abstracts International, Volume: 41-11, Section: B, page: 4175. / Thesis (Ph.D.)--The Florida State University, 1980.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_74358 |
| Contributors | PEREIRA, CARLOS ALBERTO DE BRAGANCA., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 113 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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