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Title: Bayesian consistency for regression models
Author: Xiang, Fei
Awarding Body: University of Kent
Current Institution: University of Kent
Date of Award: 2012
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Bayesian consistency is an important issue in the context of non- parametric problems. The posterior consistency is a validation of a Bayesian approach and guarantees the posterior mass accumulates around the true density, which" is unknown in most circumstances, as the number of observations goes to infinity. This thesis mainly considers the consistency for nonparametric regression models over both random and non random covariates. The techniques to achieve consistency under random covariates are similar to that derived in Walker (2003, 2004) which is designed for the consistency of independent and identically distributed variables. We contribute a new idea to deal with the supremum metric over covariates when the regression model is with non random covariates. That is, if a regression density is away from the true density in the Hellinger sense, then there is a covariate, whose value is picked from a specific design, such that the density indexed by this value is also away from the true density. As a result, the posterior concentrates in the supremum Hellinger neighbourhood of the real model under conditions on the prior such as the Kullback-Leibler property and the summability of the square rooted prior mass on Hellinger covering balls. Furthermore, the predictive is also shown to be consistent and we illustrate our results on a normal mean regression function and demonstrate the usefulness of a model based on piecewise constant functions. We also investigate conditions under which a piecewise density model is consistent.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available