Objective Bootstrap Posterior distributions

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2023-08

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This thesis presents a new way to perform Bayesian inference via a fiducial type idea. An adjustment to the derivation of the usual fiducial distribution leads to a procedure which is universally available. Further it is well motivated from both an objective probability matching procedure and the bootstrap. It is generally applicable avoiding the traditional MCMC due to its prior-free feature. The corresponding posterior is called Objective Bootstrap Posterior. Many scenarios are considered to show the competitive performance of the Objective Bootstrap Posterior, including both parametric and nonparametric cases. The thesis focuses more on the nonparametric settings, since in the parametric case there is a coincidence with the parametric bootstrap of Efron, though it has never been used as a suggested posterior itself. We also introduce a new asymptotic distribution for the maximum likelihood estimator and illustrate in several examples.

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