The Bayesian inference strategy is studied within the framework of operational statistics (generalized sample spaces). Conditions necessary and sufficient for consistency and strict consistency of a complete betting rate assignment are derived. A constructive proof is given of the existence of a unique second-order probability which induces a given consistent and countably additive complete betting rate assignment. Continuity of the Bayesian inference strategy is investigated. Asymptotic properties of the Bayesian inference strategy are examined both at the level of betting rates and at the level of second-order probabilities.
","abstract_html":"<p>The Bayesian inference strategy is studied within the framework of operational statistics (generalized sample spaces). Conditions necessary and sufficient for consistency and strict consistency of a complete betting rate assignment are derived. A constructive proof is given of the existence of a unique second-order probability which induces a given consistent and countably additive complete betting rate assignment. Continuity of the Bayesian inference strategy is investigated. Asymptotic properties of the Bayesian inference strategy are examined both at the level of betting rates and at the level of second-order probabilities.</p>","abstract_has_math":false,"creators":["MAGNESS, CAROLYN MARGARET"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1984,"date_issued":"1984-01-01T08:00:00Z","date_published":"1984-01-01T08:00:00Z","updated_at":"2026-07-24T05:23:21Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholars.unh.edu/dissertation/1429","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["MAGNESS, CAROLYN MARGARET"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholars.unh.edu/dissertation/1429"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The Bayesian inference strategy is studied within the framework of operational statistics (generalized sample spaces). Conditions necessary and sufficient for consistency and strict consistency of a complete betting rate assignment are derived. A constructive proof is given of the existence of a unique second-order probability which induces a given consistent and countably additive complete betting rate assignment. Continuity of the Bayesian inference strategy is investigated. Asymptotic properties of the Bayesian inference strategy are examined both at the level of betting rates and at the level of second-order probabilities.
"]},{"key":"dc:title","label":"Title","values":["SOME PROBLEMS IN BAYESIAN INFERENCE IN A NONCLASSICAL SETTING (OPERATIONAL STATISTICS, BETTING RATES, COHERENCE)"]}]}],"canonical_facts":{"dc:creator":["MAGNESS, CAROLYN MARGARET"],"dc:description.abstract":["The Bayesian inference strategy is studied within the framework of operational statistics (generalized sample spaces). Conditions necessary and sufficient for consistency and strict consistency of a complete betting rate assignment are derived. A constructive proof is given of the existence of a unique second-order probability which induces a given consistent and countably additive complete betting rate assignment. Continuity of the Bayesian inference strategy is investigated. Asymptotic properties of the Bayesian inference strategy are examined both at the level of betting rates and at the level of second-order probabilities.
"],"dc:identifier":["https://scholars.unh.edu/dissertation/1429"],"dc:subject":["Mathematics"],"dc:title":["SOME PROBLEMS IN BAYESIAN INFERENCE IN A NONCLASSICAL SETTING (OPERATIONAL STATISTICS, BETTING RATES, COHERENCE)"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy"]},"updated_at":"2026-07-24T05:23:21Z"}