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We shall determine values for the unknown parameters μ and σ2 in the Gaussian by maximizing the likelihood function. In practice, it is more convenient to maximize the log of the likelihood function. Because the logarithm is monotonically increasing function of its argument, maximization of the log of a function is equivalent to maximization of the function itself. Taking the log not only simplifies the subsequent mathematical analysis, but it also helps numerically because the product of a large number of small probabilities can easily underflow the numerical precision of the computer, and this is resolved by computing instead the sum of the log probabilities.
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为什么要使用log likelihood 一是计算方便，二是log对于那些小概率的事件用加和比乘积更漂亮