Approximate Behavior of the Posterior Distribution for a Large Observation
大观测值下后验分布的近似行为
Let $X$ be a real valued random variable with a family of possible distributions belonging to a one parameter exponential family with the natural parameter $\theta \in(\underline{\theta}, + \infty)$. Let $g$ be a prior probability density for $\theta$ with unbounded support. Under some additional assumptions it is shown that for large values of $x$ the posterior distribution of $\theta$ given $X = x$ is approximately normally distributed about its mode. If $\delta_g$ denotes…