“Maximum Likelihood”的概念、定义、习题解题方法及翻译-数学辞典

单词

Maximum Likelihood

释义

Maximum Likelihood

The procedure of finding the value of one or more parameters for a given statistic which makes the knownLikelihood distribution a Maximum. The maximum likelihood estimate for a parameter is denoted.

For a Bernoulli Distribution,

(1)

so maximum likelihood occurs for

. If

is not known ahead of time, the likelihood function is



			(2)

where

or 1, and

, ...,

(3)

(4)

(5)

(6)

For a Gaussian Distribution,

(7)

(8)

(9)

gives

(10)

(11)

gives

(12)

Note that in this case, the maximum likelihood Standard Deviation is the sample Standard Deviation, whichis a Biased Estimator for the population Standard Deviation.

For a weighted Gaussian Distribution,

(13)

(14)

(15)

gives

(16)

The Variance of the Mean is then

(17)

But

(18)


			(19)

For a Poisson Distribution,

(20)

(21)

(22)

(23)

See also Bayesian Analysis

References

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Least Squares as a Maximum Likelihood Estimator.'' §15.1 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 651-655, 1992.

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