Maximum Likelihood Estimation
时间: 2024-05-30 17:10:06 浏览: 11
Maximum likelihood estimation (MLE) is a statistical method used to estimate the parameters of a probability distribution by maximizing the likelihood function, which is the probability of the observed data given the parameter values. In other words, MLE seeks to find the values of the parameters that make the observed data most likely to have occurred.
For example, let's say we have a sample of data that we believe comes from a normal distribution with unknown mean and variance. We can use MLE to estimate the mean and variance of the distribution by finding the values of these parameters that maximize the likelihood of the observed data.
To do this, we first write down the likelihood function, which is the product of the probability density function of each observation in the sample. We then take the natural logarithm of the likelihood function and differentiate it with respect to each parameter. We set the resulting equations equal to zero and solve for the parameter values that maximize the likelihood function.
MLE has many applications in statistics and data science, such as in fitting regression models, clustering algorithms, and machine learning models. However, it is important to note that MLE assumes that the data come from a specific probability distribution, and may not be appropriate for all types of data.
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