Document Type	Master's Dissertation
Author	Bodvin, Liesbeth Joanna Sylvia
Email	liesbeth.bodvin@gmail.com
URN	etd-07102010-123814
Document Title	Bayesian estimation of Shannon entropy for bivariate beta priors
Degree	MSc
Department	Statistics
Supervisor	Advisor Name Title Prof A Bekker Committee Chair Prof J J J Roux Committee Co-Chair
Keywords	Bayesian estimation calibration credit risk probability of default Shannon entropy bivariate beta
Date	2010-09-02
Availability	unrestricted
Abstract Having just survived what is arguably the worst financial crisis in time, it is expected that the focus on regulatory capital held by financial institutions such as banks will increase significantly over the next few years. The probability of default is an important determinant of the amount of regulatory capital to be held, and the accurate calibration of this measure is vital. The purpose of this study is to propose the use of the Shannon entropy when determining the parameters of the prior bivariate beta distribution as part of a Bayesian calibration methodology. Various bivariate beta distributions will be considered as priors to the multinomial distribution associated with rating categories, and the appropriateness of these bivariate beta distributions will be tested on default data. The formulae derived for the Bayesian estimation of Shannon entropy will be used to measure the certainty obtained when selecting the prior parameters. © 2010, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. Please cite as follows: Bodvin, LJS 2010, Bayesian estimation of Shannon entropy for bivariate beta priors, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://upetd.up.ac.za/thesis/available/etd-07102010-123814/ > C10/529/gm
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