Likelihood Based Inference

Likelihood Based Inference is a statistical method used to estimate parameters of a probability model by maximizing the likelihood function, which measures how probable the observed data is given the parameters. It is a fundamental approach in frequentist statistics for parameter estimation, hypothesis testing, and model selection. The method relies on the likelihood principle, which states that all evidence from data about parameters is contained in the likelihood function.

Also known as: Maximum Likelihood Estimation, MLE, Likelihood Inference, Likelihood Methods, Likelihood Principle

Why learn Likelihood Based Inference?

Developers should learn Likelihood Based Inference when working on data science, machine learning, or statistical modeling projects that require robust parameter estimation from data, such as in regression analysis, time series forecasting, or probabilistic programming. It is essential for tasks like building predictive models, conducting A/B testing, or implementing algorithms that involve optimization of statistical models, as it provides a principled way to infer parameters and assess model fit.

Learning Resources

• docs: Wikipedia: Likelihood Function
• course: Coursera: Statistical Inference
• video: Khan Academy: Maximum Likelihood Estimation
• book: Book: All of Statistics by Larry Wasserman
• tutorial: Tutorial: Maximum Likelihood Estimation in R