Locally uniform prior

 

目的是为了使先验的影响降到最小。

在likelihood可评估的区间，先验概率保持基本不变，在区间之外先验概率可以忽略不计。

这样后验概率基本等于似然概率。

 

A prior distribution P is locally uniform at \(\theta_0\) if

\(\frac{P(a\sigma<\theta-\theta_0< b\sigma)}{P(0<\theta-\theta_0< \sigma)} \to ~b-a \text{ for each } a<b \text{ as } \sigma \to 0\)

 

It will be shown that the posterior distribution of \(\theta|X_\sigma\) is asymptotically \(N(X_\sigma,\sigma^2)\) , if and only if \(P(\theta)\) is locally uniform and tail-bounded.

 

Hartigan J A. Locally uniform prior distributions[J]. The Annals of Statistics, 1996, 24(1): 160-173.

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