Bayesian estimation of quantile distributions |
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Authors: | D Allingham R A R King K L Mengersen |
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Institution: | (1) Centre for Complex Dynamic Systems and Control, School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW, 2308, Australia;(2) School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW, 2308, Australia;(3) School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD, 4001, Australia |
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Abstract: | Use of Bayesian modelling and analysis has become commonplace in many disciplines (finance, genetics and image analysis, for
example). Many complex data sets are collected which do not readily admit standard distributions, and often comprise skew
and kurtotic data. Such data is well-modelled by the very flexibly-shaped distributions of the quantile distribution family,
whose members are defined by the inverse of their cumulative distribution functions and rarely have analytical likelihood
functions defined. Without explicit likelihood functions, Bayesian methodologies such as Gibbs sampling cannot be applied
to parameter estimation for this valuable class of distributions without resorting to numerical inversion. Approximate Bayesian
computation provides an alternative approach requiring only a sampling scheme for the distribution of interest, enabling easier
use of quantile distributions under the Bayesian framework. Parameter estimates for simulated and experimental data are presented. |
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Keywords: | Approximate Bayesian computation Posterior distribution Quantile distribution Response time data |
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