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<math>\hat a_{ML} = \text{max}_a ( Pr(x_i;a))</math> discrete | <math>\hat a_{ML} = \text{max}_a ( Pr(x_i;a))</math> discrete | ||
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==Maximum A-Posteriori Estimation (MAP)== | ==Maximum A-Posteriori Estimation (MAP)== | ||
Revision as of 04:10, 12 December 2008
Contents
Maximum Likelihood Estimation (ML)
$ \hat a_{ML} = \text{max}_a ( f_{X}(x_i;a)) $ continuous
$ \hat a_{ML} = \text{max}_a ( Pr(x_i;a)) $ discrete
Maximum A-Posteriori Estimation (MAP)
Minimum Mean-Square Estimation (MMSE)
$ \hat{y}_{\rm MMSE}(x) = \int\limits_{-\infty}^{\infty}\ {y}{f}_{\rm Y|X}(y|x)\, dy={E}(Y|X=x) $
Mean square error : $ MSE = E[(\theta - \hat \theta(x))^2] $
Linear Minimum Mean-Square Estimation (LMMSE)
$ \hat{y}_{\rm LMMSE}(x) = E[\theta]+\frac{COV(x,\theta)}{Var(x)}*(x-E[x]) $
Hypothesis Testing: ML Rule
Type I error
Type II error
Hypothesis Testing: MAP Rule
Overall P(err)
