Maximum Likelihood Estimation (MLE) is a statistical method used to estimate the parameters of a probability distribution, given a set of observations. The general pipeline of MLE involves the following steps:
- Define a probability distribution: The first step in MLE is to select an appropriate probability distribution that can model the data. For example, if the data is continuous, one could use a Gaussian distribution. If the data is categorical, one could use a multinomial distribution.
- Formulate the likelihood function: The likelihood function is a function that describes the probability of observing the data given the parameters of the probability distribution. It is formulated by taking the product of the probability density function (PDF) of each observation.
- Maximize the likelihood function: The next step is to find the values of the parameters that maximize the likelihood function. This is done by taking the derivative of the likelihood function with respect to each parameter, setting the derivatives to zero, and solving for the parameters.
- Evaluate the estimated parameters: Once the maximum likelihood estimates are obtained, they can be used to estimate other quantities of interest, such as the mean or variance of the distribution.
- Test the model: Finally, the estimated parameters can be used to generate predictions or simulate data to test the model’s accuracy and robustness.
Overall, the pipeline of MLE involves selecting an appropriate probability distribution, formulating the likelihood function, maximizing the likelihood function to estimate the parameters, evaluating the estimated parameters, and testing the model’s performance.