maximum likelihood estimation: meaning, definition, pronunciation and examples
C2Formal, Technical, Academic
Quick answer
What does “maximum likelihood estimation” mean?
A method in statistics for estimating the parameters of a statistical model, selecting the parameter values that maximize the likelihood function (i.
Audio
Pronunciation
Definition
Meaning and Definition
A method in statistics for estimating the parameters of a statistical model, selecting the parameter values that maximize the likelihood function (i.e., the probability of observing the given data).
A fundamental inference procedure where parameter estimates are chosen to make the observed sample data most probable under an assumed probability model. It is a cornerstone of frequentist statistics, with widespread applications in machine learning, econometrics, and scientific modeling.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or syntactic differences. Spelling follows regional conventions (e.g., BrE 'likelihood', AmE 'likelihood'—same spelling). Pronunciation may differ slightly.
Connotations
Identical technical connotations in both varieties.
Frequency
Equally frequent in academic and technical contexts in both regions.
Grammar
How to Use “maximum likelihood estimation” in a Sentence
[Subject] performs maximum likelihood estimation on [data] to estimate [parameters].Maximum likelihood estimation of [parameter] yields [result].We employed maximum likelihood estimation.The estimates were obtained by maximum likelihood estimation.Vocabulary
Collocations
Examples
Examples of “maximum likelihood estimation” in a Sentence
verb
British English
- To fit the model, we need to maximise the likelihood function.
- The parameters were estimated by maximising the likelihood.
American English
- To fit the model, we need to maximize the likelihood function.
- We estimated the parameters using likelihood maximization.
adverb
British English
- The parameters were estimated maximum-likelihood.
- This is not typically used adverbially.
American English
- The parameters were estimated via maximum likelihood.
- This is not typically used adverbially.
adjective
British English
- The maximum-likelihood approach is standard.
- She presented the maximum-likelihood results.
American English
- The maximum likelihood approach is standard.
- She presented the maximum likelihood results.
Usage
Meaning in Context
Business
Rare, except in specialized quantitative finance or market research analytics.
Academic
Ubiquitous in statistics, econometrics, biostatistics, psychology, and machine learning papers and textbooks.
Everyday
Virtually never used.
Technical
Core terminology in data science, engineering, and any field involving statistical modeling and inference.
Vocabulary
Synonyms of “maximum likelihood estimation”
Strong
Neutral
Weak
Vocabulary
Antonyms of “maximum likelihood estimation”
Watch out
Common Mistakes When Using “maximum likelihood estimation”
- Saying 'maximum likelihood estimator' when referring to the method (estimation) rather than the resulting formula (estimator).
- Confusing it with 'maximum a posteriori estimation' (MAP), which incorporates prior beliefs.
- Using it as a verb: Incorrect: 'We will maximum likelihood estimate the parameter.' Correct: 'We will estimate the parameter using maximum likelihood.'
FAQ
Frequently Asked Questions
The main idea is to choose the parameter values for a model that make the observed sample data you have collected the most probable or 'likely' to have occurred.
No. MLE is a frequentist method that uses only the observed data. Bayesian estimation incorporates prior beliefs about the parameters (a prior distribution) and updates them with the data to form a posterior distribution.
It refers to how the MLE behaves as the sample size becomes very large. Key asymptotic properties include consistency (it converges to the true parameter value), normality (its distribution becomes normal), and efficiency (it achieves the lowest possible variance among consistent estimators).
MLE can be problematic with very small sample sizes, when the likelihood function is flat or has multiple maxima, when computational complexity is too high, or when a full probabilistic model for the data cannot be or is not specified.
A method in statistics for estimating the parameters of a statistical model, selecting the parameter values that maximize the likelihood function (i.
Maximum likelihood estimation is usually formal, technical, academic in register.
Maximum likelihood estimation: in British English it is pronounced /ˌmæk.sɪ.məm ˈlaɪ.kli.hʊd ˌes.tɪˈmeɪ.ʃən/, and in American English it is pronounced /ˌmæk.sə.məm ˈlaɪ.kli.hʊd ˌes.təˈmeɪ.ʃən/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “The gold standard of estimation (informal, context-dependent)”
Learning
Memory Aids
Mnemonic
Think of a detective (the estimator) looking for the most LIKELY suspect (parameter value) based on the MAXIMUM amount of evidence (data).
Conceptual Metaphor
ESTIMATION IS A SEARCH (for the best parameter value). LIKELIHOOD IS A HEIGHT (to be maximized on a surface).
Practice
Quiz
Maximum likelihood estimation is primarily associated with which statistical paradigm?