Large Deviation Principles for Posterior Distributions of the Normal Parameters

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Suppose that X1,X2,... are conditionally i.i.d. random variables with distribution Pθ given ＝θ，where is an unknown parameter. If Pθ is a normal distribution with mean θ and known variance σ2, and if the prior of is chosen from the conjugate family N(μ,v2) or proportional to the Lebesgue measure, then it follows that the posterior distributions given X1,...,Xn obey a large deviation principle with a rate function. If Pθ is a normal distribution with known mean and unknown precision θ, and if as a prior we choose the gamma distribution with parameters α and β or the improper distribution (1/θ)dθ，the Jeffereys' prior, then the posterior distributions of given X1,...,Xn are shown to satisfy a large deviation principle. The G artner-Ellis theorem plays the key role to prove these large deviation principles for the posterior distributions.

經營と經濟, vol.91(4), pp.149-160; 2012

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  • 経営と経済

    経営と経済 91 (4), 149-160, 2012-03-25

    長崎大学経済学会

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