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Science Forum Index » Statistics - Education Forum » Bayesian updating of information
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| Guest |
 Posted: Mon Feb 12, 2007 8:48 am |
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I have measurements that is summarized by mean mu, variance V and
number of observations n. For sufficiency reasons I model the data
through empirical means y_hat which depend on an unknown parameter
theta as follows (with variance V assumed known)
y_hat | theta ~ N(theta, V/n)
The prior knowledge is incorporated in a distribution as
theta ~ N(mu0, V0 / n0)
reflecting information from n0 prior measurements each having mean
mu0
and variance V0
The posterior becomes
theta | y_hat ~ N(mu_post, V_post) with
mu_post = (n0/V0 * mu0 + n/V * y_hat) / (n0/V0 + n/V)
and
V_post = 1 / (n0/V0 + n/V).
Assuming the posterior has the same form as the prior, what
interpretation of V_post * (n0+n) can be made? Is it a good estimate
of posterior variance of a single measurement? |
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