Maximum Likelihood Estimation
May 1, 2024
3 minute read
Maximum likelihood estimation (MLE) is a statistical method used to estimate the parameters of a probability distribution by maximizing the likelihood function. The likelihood function measures the compatibility of the observed data with different possible values of the parameters. By finding the values of the parameters that maximize the likelihood function, we can obtain the most plausible explanation for the observed data.
Theory of Maximum Likelihood Estimation
The theory of MLE is based on the assumption that the observed data is a sample from a population that follows a known probability distribution. The parameters of the distribution are unknown, and the goal of MLE is to estimate these parameters from the observed data.
Likelihood Function
The likelihood function is a function of the parameters of the distribution that measures the probability of observing the data given those parameters. By maximizing the likelihood function, we can find the values of the parameters that make the observed data most likely.
MLE Estimator
The MLE estimator is the value of the parameters that maximizes the likelihood function. This estimator is consistent, meaning that it converges to the true value of the parameters as the sample size increases.
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Reading list
We've selected 11 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Maximum Likelihood Estimation.
This advanced textbook covers machine learning algorithms and theory from a probabilistic perspective. It includes a comprehensive discussion of MLE and its applications in machine learning.
This advanced monograph provides a detailed and rigorous treatment of MLE, including its theoretical properties and applications. It is written for researchers and advanced students with a strong background in statistics.
This advanced textbook provides a rigorous and in-depth treatment of likelihood and Bayesian inference, including a detailed discussion of MLE.
This widely-used textbook provides a practical introduction to statistical learning methods, including MLE. It is written in a clear and accessible style, making it suitable for beginners and experienced practitioners alike.
This classic textbook provides a rigorous and in-depth treatment of statistical models, including a detailed discussion of MLE and its properties.
This textbook provides a comprehensive overview of machine learning algorithms, including a detailed discussion of MLE and its applications in machine learning.
This textbook provides a comprehensive overview of computational methods used in statistics, including MLE. It covers a wide range of topics, from basic statistical concepts to advanced computational techniques.
This comprehensive textbook provides a thorough introduction to Bayesian data analysis, including a detailed discussion of MLE and its relationship to Bayesian inference.
This textbook provides a comprehensive overview of modern statistical methods, including a detailed discussion of MLE and its applications. It is written in a clear and concise style, making it accessible to a wide audience.
This introductory textbook provides a clear and concise overview of modern statistical methods, including MLE. It is suitable for students with a basic understanding of probability and statistics.
This introductory textbook provides a clear and concise overview of likelihood-based statistical methods, including MLE. It is written in a non-technical style, making it accessible to a wide audience.
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