FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2890141283> ?p ?o ?g. }

• W2890141283 abstract "Bayesian inference is, by far, the most well-known statistical method for updating beliefsabout a population feature of interest in light of new data. Current beliefs, characterized by aprobability distribution called a prior, are updated by combining with data, which is modeledas a random draw from another probability distribution. The Bayesian framework, therefore,depends heavily on the choices of model distributions for prior and data, and it is the latterthat is of particular concern in this dissertation. Often, as will be shown in various examples, it is particularly difficult to make a good choice of data model: a bad choice may lead to misspecification and inconsistency of the posterior distribution, or may introduce nuisance parameters, increasing computational burden and complicating the choice of prior. Some particular statistical problems that may give Bayesians pause are classification and quantile regression. In these two problems a mathematical function called a loss function serves as the natural connection between the data and the population feature. Statistical inference based on loss functions can avoid having to specify a probability model for the data and parameter, which may be incorrect. Bayes' Theorem cannot reconcile a posterior update using anything other than a probability model for data, so alternative methods are needed, besides Bayes, in order to take advantage of loss functions in these types of problems.Gibbs posteriors, like Bayes posteriors, incorporate prior information and new data via an updating formula. However, the Gibbs posterior does not require modeling the data with a probability model as in Bayes; rather, data and parameter may be linked by a more general function, like the loss functions mentioned above. The Gibbs approach offers many potential benefits including robustness when the data distribution is not known and a natural avoidance of nuisance parameters, but Gibbs posteriors are not common throughout statistics literature. In an effort to raise awareness of Gibbs posteriors, this dissertation both develops new theoretical foundations and presents numerous examples highlighting the usefulness of Gibbs posteriors in statistical applications.Two new asymptotic results for Gibbs posteriors are contributed. The main conclusion of the first result is that Gibbs posteriors have similar asymptotic behavior to a class of statistical estimators called M-estimators in a wide range of problems. The main advantage of the Gibbs posterior, then, is its ability to incorporate prior information. The second result extends results for Bayesian posteriors to Gibbs posteriors in a statistics problems where the population feature of interest is a set with a smooth boundary.Additionally, two main applications are considered, one in medical statistics and one in image analysis. The first application concerns the minimum clinically important difference (MCID), a parameter designed to indicate whether the effect of a medical treatment is practically signi cant. Modeling for the purpose of inference on the MCID is non-trivial, and concernsabout bias from a misspeci fied parametric model or inefficiency from a nonparametric model motivate using the alternative Gibbs approach, which balances robustness and efficiency. The second application concerns the detection of an image boundary when the image pixels are observed with noise. Likelihood-based methods for the image boundary require modeling the pixel intensities inside and outside the image boundary, even though these are typically of no practical interest. However, a Gibbs posterior can be defined directly on the image boundary parameter, thereby avoiding this issue.Finally, the Gibbs posterior comes with a scale parameter, also referred to as a learning rate, which mainly affects its finite sample performance. Current research directions do not agree on how to select the learning rate. This dissertation presents a new method, called Gibbs posterior calibration (GPC), to select the learning rate so that Gibbs posterior credible regions are approximately calibrated to their nominal frequency coverage probabilities. Simulation results demonstrate that the proposed algorithm yields highly efficient credible regions in a variety of applications when compared to existing methods." @default.
• W2890141283 created "2018-09-27" @default.
• W2890141283 creator A5070473780 @default.
• W2890141283 date "2017-11-22" @default.
• W2890141283 modified "2023-09-23" @default.
• W2890141283 title "Gibbs Posterior Distributions: New Theory and Applications" @default.
• W2890141283 hasPublicationYear "2017" @default.
• W2890141283 type Work @default.
• W2890141283 sameAs 2890141283 @default.
• W2890141283 citedByCount "1" @default.
• W2890141283 countsByYear W28901412832021 @default.
• W2890141283 crossrefType "dissertation" @default.
• W2890141283 hasAuthorship W2890141283A5070473780 @default.
• W2890141283 hasConcept C105795698 @default.
• W2890141283 hasConcept C107673813 @default.
• W2890141283 hasConcept C119857082 @default.
• W2890141283 hasConcept C134261354 @default.
• W2890141283 hasConcept C138885662 @default.
• W2890141283 hasConcept C144024400 @default.
• W2890141283 hasConcept C149441793 @default.
• W2890141283 hasConcept C149782125 @default.
• W2890141283 hasConcept C149923435 @default.
• W2890141283 hasConcept C154945302 @default.
• W2890141283 hasConcept C158424031 @default.
• W2890141283 hasConcept C160234255 @default.
• W2890141283 hasConcept C177769412 @default.
• W2890141283 hasConcept C191413810 @default.
• W2890141283 hasConcept C207201462 @default.
• W2890141283 hasConcept C2776214188 @default.
• W2890141283 hasConcept C2776401178 @default.
• W2890141283 hasConcept C2908647359 @default.
• W2890141283 hasConcept C33923547 @default.
• W2890141283 hasConcept C41008148 @default.
• W2890141283 hasConcept C41895202 @default.
• W2890141283 hasConcept C57830394 @default.
• W2890141283 hasConceptScore W2890141283C105795698 @default.
• W2890141283 hasConceptScore W2890141283C107673813 @default.
• W2890141283 hasConceptScore W2890141283C119857082 @default.
• W2890141283 hasConceptScore W2890141283C134261354 @default.
• W2890141283 hasConceptScore W2890141283C138885662 @default.
• W2890141283 hasConceptScore W2890141283C144024400 @default.
• W2890141283 hasConceptScore W2890141283C149441793 @default.
• W2890141283 hasConceptScore W2890141283C149782125 @default.
• W2890141283 hasConceptScore W2890141283C149923435 @default.
• W2890141283 hasConceptScore W2890141283C154945302 @default.
• W2890141283 hasConceptScore W2890141283C158424031 @default.
• W2890141283 hasConceptScore W2890141283C160234255 @default.
• W2890141283 hasConceptScore W2890141283C177769412 @default.
• W2890141283 hasConceptScore W2890141283C191413810 @default.
• W2890141283 hasConceptScore W2890141283C207201462 @default.
• W2890141283 hasConceptScore W2890141283C2776214188 @default.
• W2890141283 hasConceptScore W2890141283C2776401178 @default.
• W2890141283 hasConceptScore W2890141283C2908647359 @default.
• W2890141283 hasConceptScore W2890141283C33923547 @default.
• W2890141283 hasConceptScore W2890141283C41008148 @default.
• W2890141283 hasConceptScore W2890141283C41895202 @default.
• W2890141283 hasConceptScore W2890141283C57830394 @default.
• W2890141283 hasLocation W28901412831 @default.
• W2890141283 hasOpenAccess W2890141283 @default.
• W2890141283 hasPrimaryLocation W28901412831 @default.
• W2890141283 hasRelatedWork W1828441782 @default.
• W2890141283 hasRelatedWork W1949678636 @default.
• W2890141283 hasRelatedWork W1975496562 @default.
• W2890141283 hasRelatedWork W2090715958 @default.
• W2890141283 hasRelatedWork W2269971303 @default.
• W2890141283 hasRelatedWork W2292840578 @default.
• W2890141283 hasRelatedWork W2533288550 @default.
• W2890141283 hasRelatedWork W2761940481 @default.
• W2890141283 hasRelatedWork W2964096787 @default.
• W2890141283 hasRelatedWork W3029541581 @default.
• W2890141283 hasRelatedWork W3041882334 @default.
• W2890141283 hasRelatedWork W3101417746 @default.
• W2890141283 hasRelatedWork W3103181734 @default.
• W2890141283 hasRelatedWork W3104566134 @default.
• W2890141283 hasRelatedWork W3118592089 @default.
• W2890141283 hasRelatedWork W3166714389 @default.
• W2890141283 hasRelatedWork W3183471713 @default.
• W2890141283 hasRelatedWork W3198718921 @default.
• W2890141283 hasRelatedWork W50255772 @default.
• W2890141283 hasRelatedWork W3126972261 @default.
• W2890141283 isParatext "false" @default.
• W2890141283 isRetracted "false" @default.
• W2890141283 magId "2890141283" @default.
• W2890141283 workType "dissertation" @default.