The most plausible estimate is that
use of known sample results，
the inverse is the most likely (maximum probability) of a parameter value that results in such a result.
For example: A sack with a white ball and a black ball, but I do not know the ratio between them, then I have put back the extraction 10 times, and I found that I smoked 8 black ball 2 times the white ball, I asked the most likely between the black and white ball ratio when the maximum likelihood estimation method is taken: I suppose I'm the probability of a black ball being p, That's 8 black balls, 2 white balls. The probability of the result is:
P (Black =8) =p^8* (1-p) ^2, now I want to draw a p is how much ah, very simple, so that P (black =8) the largest p is the result of my request, then the process of derivation is the process of finding the extremum.
Maybe you'll have questions,Why LN, this is because ln multiplies multiplication into addition and does not change the position of the extremum (monotonic consistency) .~
Similarly, this topic: set the overall
XThe probability density is
Known x1,x2: Xn is the sample observation value, and the maximum likelihood estimation of θ is obtained.
That's the same thing, to get x1,x2. The probability of xn such a set of sample observations is
P{x1=x1,x2=x2,... xn=xn}=f (x1,θ) F (x2,θ) ... f (xn,θ)
Then we ask to make P the largest θ is good, the same is the process of seeking extreme value, no longer repeat.
King of Slag
Links: https://www.zhihu.com/question/20447622/answer/23902715
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Copyright belongs to the author, please contact the author for authorization. Least squares: A (group) estimate is found so that the actual value is minimized from the estimated value. It is desirable to summarize and minimize the absolute value of the difference, but it is troublesome to find the minimum in mathematics, so the alternative is to look for a (group) estimate so that the sum of the squares of the difference between the actual and the estimated values is the smallest, called the least squares. "Least square" in English, in fact, the literal meaning of English is "the smallest square." At this point, the sum of the squared difference to the parameter derivative number, and take the first derivative of zero, is olse.
Rice Floral
Links: https://www.zhihu.com/question/20447622/answer/23848605
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Copyright belongs to the author, please contact the author for authorization. First, the conclusion: the least square method is equivalent to the maximum likelihood estimation in the case of the error obeying the Gaussian distribution. The least squares method is derived from the least squares based on the maximum likelihood estimation.
Objective: To predict unknown data through existing data. Generally, a linear equation with multiple variables is made.
Principle: Suppose that in a 2-dimensional coordinate, there are many points, we have a straight line, the line satisfies: coordinates all points to the line distance and the smallest. (Note that this distance is not an excessive point in the line to make a vertical line, but rather than the point to do a parallel to the y-axis lines, the distance formed)
Finally, in a lot of data analysis, people tend to be more willing to use "distance" to describe the relationship between numbers and numbers, and what is the Markov distance method, generalized square distance method, etc.
Mi Total
Links: https://www.zhihu.com/question/20447622/answer/15732404
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Copyright belongs to the author, please contact the author for authorization.
Maximum Likelihood method understanding
