%0 Book
%T Bernstein-von Mises Theorem for a group testing problem
%A Kunick, Jonathan
%D 2024
%C Rostock
%C Universität Rostock
%G English
%F 1969479183
%O vorgelegt von Jonathan Kunick
%O GutachterInnen: Alexander Meister (Universität Rostock) ; Ismael Castillo (Sorbonne Université Paris)
%O Dissertation Universität Rostock 2024
%X We propose a Bayesian model to investigate a group testing regression model of equally- sized subgroups. The group testing design was developed by Dorfman (1943) to reduce costs and increase efficiency when detecting illnesses in populations and can be used to detect contamination in samples, when prevalence is low enough. We develop a Laplace-Bernstein- von Mises (BvM) Theorem in the style of Le Cam (1986), where distributional convergence to a Gaussian holds in total variation distance almost surely, and we list sufficient conditions. We also deduce additional conditions to derive a strong BvM for the group testing posterior distribution.<eng>
%L 310
%9 theses
%9 Text
%9 Hochschulschrift
%R 10.18453/rosdok_id00005404
%U https://purl.uni-rostock.de/rosdok/id00005404
%U https://nbn-resolving.org/urn:nbn:de:gbv:28-rosdok_id00005404-2
%U https://d-nb.info/1397495227/34
%U https://doi.org/10.18453/rosdok_id00005404