Maximum-likelihood estimation is best described as?

Maximum-likelihood estimation is best described as?

• A. It estimates parameters by maximizing the probability of observing the data.
• B. It minimizes the sum of squared errors.
• C. It uses prior distributions to update beliefs.
• D. It samples parameters randomly.

Answer: (A)

Maximum-likelihood estimation finds the parameter values that make the observed data most probable. You set up a likelihood function that expresses the probability of the data given the parameters, and you choose the parameters that maximize this likelihood (often by maximizing the log-likelihood for mathematical convenience). This approach focuses on how well the chosen model explains the actual data. Minimizing the sum of squared errors is a different criterion tied to least squares, usually under specific assumptions about error structure; it’s not the general idea of MLE. Using prior distributions to update beliefs is Bayesian inference, which combines priors with data to form a posterior. Sampling parameters randomly describes stochastic search methods or Bayesian sampling, not the deterministic optimization MLE performs. For example, with normally distributed data and known variance, the MLE for the mean is the sample mean, illustrating how the observed data directly drive the parameter estimate through the likelihood.

Maximum-likelihood estimation finds the parameter values that make the observed data most probable. You set up a likelihood function that expresses the probability of the data given the parameters, and you choose the parameters that maximize this likelihood (often by maximizing the log-likelihood for mathematical convenience). This approach focuses on how well the chosen model explains the actual data.

Minimizing the sum of squared errors is a different criterion tied to least squares, usually under specific assumptions about error structure; it’s not the general idea of MLE. Using prior distributions to update beliefs is Bayesian inference, which combines priors with data to form a posterior. Sampling parameters randomly describes stochastic search methods or Bayesian sampling, not the deterministic optimization MLE performs. For example, with normally distributed data and known variance, the MLE for the mean is the sample mean, illustrating how the observed data directly drive the parameter estimate through the likelihood.