A = -, = E(010) = + c oan (HeO ' + c,„)--' ( 0 - Hp(? : which is the classic estimator. 5.7.2 Bayesian linear model Now consider the Bayesian linear model (for which the MMSE computation is also rel- atively easy): o = HO + w, where 0 is the unknown (random) parameter to be estimated with prior PDF AT(µ0, Co) c90 coo j L / x k / x / then the conditional PDF, p(OIo), is also Gaussian and: E(01o) = Applying this property to o and 0 that are jointly Gaussian in the Bayesian linear model,

doi:10.1201/9781482276237-30

Chapter

A = -, = E(010) = + c oan (HeO ' + c,„)--' ( 0 - Hp(?

Chapter

ABSTRACT

For the Gaussian posterior PDF it should be noted that the mean, median and mode are identical. Of most interest are the quadratic and hit-or-miss cost functions which, together with a special case of the latter, yield the following three important classes of estimators:

1. MMSE (Minimum Mean Square Error) estimator which we have already introduced as the conditional expectation:

o = f Op(9lo)(10.