Maximum a posteriori maximum likelihood estimation &

The problem is that the known sample results D, seeking the maximum probability of the parameter $ \ theta $

Maximum a posteriori (MAP):

Seeking the $ P (\ theta | D) $ largest $ \ theta $;

$P(\theta |D)=\frac{P(D|\theta )P(\theta )}{P(D)}$

Wherein, P (D) is a known quantity, a constant, because the sample results have been set up;

Request $ max P (\ theta | D) $, corresponds to seek $ max {P (D | \ theta) P (\ theta)} $

 

Maximum likelihood estimation (MLE):

Equivalent to seeking $ P (\ theta) $ $ maxP time is uniformly distributed (\ theta | D) $;

I.e. seeking $ max {P (D | \ theta) $;

Likelihood function $ l (\ theta) = P (D | \ theta) = P (x_ {1}, ..., x_ {N} | \ theta) = \ prod_ {i = 1} ^ {N} P (x_ {i} | \ theta) $

Known samples D, each independently seek between $ \ theta $, samples;

Solution: Demand $ Ln ​​(l (\ theta)) $, then partial derivatives, $ \ frac {\ partial Ln (l (\ theta))} {\ partial \ theta} $