Maximum Likelihood Estimation

The maximum likelihood estimation method is another method for estimating. in 1821, the German mathematician C. f. gauss proposed, but this method is often attributed to the British statistician R. a. fisher, his 1922 paper on the mathematical foundations of theoretical statistics, reprinted in contributions to Mathematical Statistics (by R. a. fisher), 1950, J. wiley & Sons, New York, once again put forward this idea, and first explored some properties of this method. the name of the maximum likelihood estimation is also provided by the rest. This method is still widely used. It is a statistical method based on the maximum likelihood principle. The intuitive idea of the maximum likelihood principle is: a random test has several possible results, such as A, B, C ,.... If result a appears in a test, it is generally considered that the test condition is favorable for A, that is, a has a high probability of.

General steps to evaluate the maximum likelihood function:

(1) write the likelihood function;

(2) Take the logarithm of the likelihood function and sort it out;

(3) derivative; (4) solutions to the Likelihood Equation

Maximum Likelihood Estimation is only an application of Probability Theory in statistics. It is one of the parameter estimation methods. It is said that a random sample is known to satisfy a certain probability distribution, but the specific parameters are not clear. The parameter estimation is based on several tests, the results are observed, and the approximate values of the parameters are introduced using the results. The maximum likelihood estimation is based on the idea that it is known that a parameter can maximize the probability of this sample. Of course, we will not choose other samples with low probability, therefore, we can simply use this parameter as the estimated real value.

Of course, the maximum likelihood estimation is just a rough mathematical expectation. To know its error size, we need to make an interval estimation.

Additional reading:

• 1Http://zhidao.baidu.com/question/33787680.html? SI = 5 & WTP = wk
• 2Mathematical Statistics-basic concepts and topics
• 3Peter J. Bickel, K. A. daoksu
• 4Translated by Li Zehui, Wang Jialing, and Lin Heng
• 5Lanzhou University Press, 2004

Open classification: mathematics, openness, probability, statistical method, and maximum likelihood principle

From: http://baike.baidu.com/view/185250.htm