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Last edited on
Jun 20, 2025 by JJ.
Jan JOHANNES Mar 05,2025 Theses
Thesis:
Bachelor in Mathematics

Author:
Svenja Fischer

Title:
Asymptotische Normalität von a-posteriori Verteilungen

Supervisor:
Jan JOHANNES

Abstract:
In this bachelorthesis, we study the posterior probability distribution of exponential families when the dimension of the parameter tends to infinity. We show, that under certain conditions the posterior probability distribution is asymptotically normal. Those conditions are based on the prior distribution and the growth rate of the dimension. In the beginning we review a few basics of probability theory and statistics. Then we proof the asymptotic normality. In the end we apply the results to the estimation of the mean vector of an infinite dimensional normal distribution.

References:
S Ghosal. Asymptotic normality of posterior distributions for exponential families when the number of parameters tends to infinity, Journal of Multivariate Analysis, 74(1):49–68, 2000.