What is Likelihood Estimation?

What is Likelihood Estimation?

Likelihood Estimation is a statistical method used to estimate the parameters of a probability distribution or a statistical model based on observed data. Unlike traditional estimation methods that focus on finding the “best-fitting” parameters, likelihood estimation frames the problem in terms of the likelihood function....

What is Maximum Likelihood Estimation (MLE)?

The goal of likelihood estimation is to find the parameter values that maximize the likelihood function. These parameter values are called Maximum Likelihood Estimates (MLEs). Once the MLEs are obtained, they provide estimates of the parameters that best explain the observed data. These estimates can be used for inference, prediction, or further analysis depending on the context of the problem....

Conclusion

Maximum Likelihood Estimation (MLE) is a vital tool for statistical modeling, especially in parameter estimation from observed data. In our exploration, we focused on Likelihood Estimation’s essence, implementing it practically using R for linear regression with earthquake data. We covered data preparation, likelihood function definition, optimization, and result interpretation. Assessing model fit involved residual analysis, R-squared, hypothesis testing, and visual assessment. We also discussed handling constraints and bounds for parameter validity. Advanced techniques like regularization, feature engineering, and ensemble methods were highlighted, showcasing MLE’s pivotal role in model building and insight derivation....