Part of Speech

The phrase "generalized maximum likelihood" functions primarily as a noun in statistical and mathematical contexts.

Phonetic Transcription

/gɛnəˌraɪzd ˈmæksɪməm ˈlaɪklihʊd/

Meaning and Usage

"Generalized maximum likelihood" refers to a broad statistical method used for estimating parameters in statistical models by maximizing the likelihood function. This technique allows for the incorporation of more complex models compared to traditional maximum likelihood approaches, making it particularly useful in various fields such as econometrics, machine learning, and bioinformatics.

• Frequency of Use: This term is more frequently encountered in written academic and professional settings, particularly in research papers, textbooks, and statistical analysis reports.

Example Sentences: 1. The researchers applied the generalized maximum likelihood method to estimate the model parameters accurately. - Исследователи применили метод обобщенного максимального правдоподобия для точной оценки параметров модели.

1. Generalized maximum likelihood provides a robust framework for dealing with various types of data distributions.

2. Обобщенное максимальное правдоподобие предоставляет надежную основу для работы с различными типами распределений данных.

3. The effectiveness of generalized maximum likelihood in high-dimensional data analysis has been widely acknowledged in recent studies.

4. Эффективность обобщенного максимального правдоподобия в анализе данных высокой размерности была широко признана в последних исследованиях.

Idiomatic Expressions

The phrase "generalized maximum likelihood" is specific to technical jargon in statistics and does not commonly appear in idiomatic expressions. However, the concept of "maximum likelihood" can be found in broader discussions about statistical estimation and modeling.

Example Sentences with Similar Expressions: 1. The principle of maximum likelihood is often used to obtain estimates that are statistically efficient. - Принцип максимального правдоподобия часто используется для получения оценок, которые статистически эффективны.

1. Maximizing the likelihood function is crucial for deriving meaningful insights from large datasets.

2. Максимизация функции правдоподобия имеет решающее значение для получения значимых выводов из больших наборов данных.

3. Understanding maximum likelihood estimation can significantly improve your capabilities in statistical modeling.

4. Понимание оценки максимального правдоподобия может значительно улучшить ваши способности в статистическом моделировании.

Etymology

The term "maximum likelihood" originates from the field of statistics. "Maximum" comes from the Latin word 'maximus', meaning "greatest," while "likelihood" derives from the Old English 'lice', meaning "manner or way" and 'hood', a suffix indicating a state of being. The combination reflects the concept of identifying the most plausible parameters under a given statistical model.

Synonyms and Antonyms

Synonyms: - Maximum likelihood estimation - Likelihood-based inference

Antonyms: - Minimum likelihood (if considering the idea of minimizing rather than maximizing) - Least squares method (as an alternative estimation technique)