期刊名称：Finance Publications / Centre for Financial Research, Cambridge University
出版年度：2007
卷号：2007
出版社：Cambridge University
摘要：Bayesian analysis offers a way of dealing with information conceptually different from all other
statistical methods. It provides a method in which observations are used to update estimates of the
unknown parameters of a statistical model. With the Bayesian approach we start with a
parametric model that is adequate to describe the phenomenon we wish to analyze. Then we
assume a prior distribution for the unknown parameters of the model θ which represent our
previous knowledge or belief about the phenomenon before observing any data. After observing
some data assumed to be generated by our model we update these assumptions or beliefs. This is
done by applying Bayes’ theorem to obtain a posterior probability density for the unknown
parameters given by
( | ) ( | ) ( )
( | ) ( )
p x p x p
px p d
θ θ
θ =
∫ θ θ θ
,
where θ is the vector of unknown parameters governing our model, p(θ ) is the prior sampling
density function of θ and x is a sample drawn from the “true” underlying distribution with
sampling density p(x | θ) that we model. Thus the posterior distribution for θ takes into account
both our prior distribution for θ and the observed data x.
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