Which estimation method selects model parameters to maximize the probability of observing the given data under a presumed data-generating process?

Which estimation method selects model parameters to maximize the probability of observing the given data under a presumed data-generating process?

• A. Residual Sum of Squares (RSS)
• B. Maximum Likelihood Estimation (MLE)
• C. Ordinary Least Squares (OLS)
• D. Deep Q-learning

Answer: (B)

Maximizing the likelihood of the observed data given the model is the idea here. You write down a likelihood function L(θ) = P(data | θ) that describes how probable the observed data are for any choice of parameters θ, and you pick the θ that makes that probability as large as possible. In practice, you often maximize the log-likelihood since the log function is monotone and it converts products into sums, making the math easier while preserving the solution. This approach, maximum likelihood estimation, yields parameter values that make the observed data most probable under the assumed data-generating process and has desirable theoretical properties under regular conditions. For contrast, residual-sum-squares focuses on minimizing the differences between observed and predicted values, which is the basis of least squares. Ordinary least squares is a specific estimator for linear models with Gaussian errors and can align with maximum likelihood in that setting, but it’s not the general principle being described. Deep Q-learning, on the other hand, is a reinforcement learning method for learning decision policies, not a parameter-estimation technique for probabilistic data.

Maximizing the likelihood of the observed data given the model is the idea here. You write down a likelihood function L(θ) = P(data | θ) that describes how probable the observed data are for any choice of parameters θ, and you pick the θ that makes that probability as large as possible. In practice, you often maximize the log-likelihood since the log function is monotone and it converts products into sums, making the math easier while preserving the solution. This approach, maximum likelihood estimation, yields parameter values that make the observed data most probable under the assumed data-generating process and has desirable theoretical properties under regular conditions.

For contrast, residual-sum-squares focuses on minimizing the differences between observed and predicted values, which is the basis of least squares. Ordinary least squares is a specific estimator for linear models with Gaussian errors and can align with maximum likelihood in that setting, but it’s not the general principle being described. Deep Q-learning, on the other hand, is a reinforcement learning method for learning decision policies, not a parameter-estimation technique for probabilistic data.