maximum likelihood: meaning, definition, pronunciation and examples
C1-C2 (Specialized)Technical/Academic
Quick answer
What does “maximum likelihood” mean?
In statistics and probability theory, the method or principle of selecting the parameter values of a model that make the observed data most probable.
Audio
Pronunciation
Definition
Meaning and Definition
In statistics and probability theory, the method or principle of selecting the parameter values of a model that make the observed data most probable.
A fundamental approach to parameter estimation and model fitting, central to frequentist inference, where the 'best' explanation is the one that maximizes the probability of the observed outcomes under the assumed model.
Dialectal Variation
British vs American Usage
Differences
No significant difference in meaning or usage. Spelling of related terms may follow regional conventions (e.g., 'parameterise' vs. 'parameterize').
Connotations
Neutral, technical term in both varieties.
Frequency
Equally common in academic and professional statistics contexts in both the UK and US.
Grammar
How to Use “maximum likelihood” in a Sentence
The maximum likelihood of [NOUN PHRASE] is...We estimated the parameters via maximum likelihood.To calculate/find/determine the maximum likelihood...The maximum likelihood estimator for [PARAMETER]...Vocabulary
Collocations
Examples
Examples of “maximum likelihood” in a Sentence
verb
British English
- The parameters were maximum-likelihooded using an iterative algorithm.
- We need to maximum-likelihood this model.
American English
- The parameters were maximum-likelihooded using specialized software.
- They maximum-likelihooded the regression coefficients.
adverb
British English
- The parameters were estimated maximum-likelihoodly.
- The model was fitted maximum-likelihoodly.
American English
- The coefficients were derived maximum-likelihoodly.
- It was optimised maximum-likelihoodly.
adjective
British English
- The maximum-likelihood estimates were computed.
- They performed a maximum-likelihood analysis.
American English
- The maximum-likelihood estimator is consistent.
- This is the maximum-likelihood solution.
Usage
Meaning in Context
Business
Rare, except in highly quantitative fields like econometrics or data science for predictive modeling.
Academic
Core term in statistics, econometrics, machine learning, biostatistics, and any field using quantitative model fitting.
Everyday
Virtually never used.
Technical
Standard, foundational term in statistics, data science, and engineering for parameter estimation.
Vocabulary
Synonyms of “maximum likelihood”
Strong
Neutral
Weak
Vocabulary
Antonyms of “maximum likelihood”
Watch out
Common Mistakes When Using “maximum likelihood”
- Using 'maximum likelihood' as an adjective without a following noun (e.g., 'We used maximum likelihood' is correct; 'We used the maximum likelihood method' is clearer).
- Confusing 'maximum likelihood estimator' (the rule/formula) with 'maximum likelihood estimate' (the numerical result).
FAQ
Frequently Asked Questions
No. Probability refers to the chance of data given known parameters. Likelihood refers to the 'plausibility' of parameters given observed data. Maximum likelihood finds the parameters that maximize this plausibility.
It is ubiquitous in statistical model fitting, including regression, machine learning (e.g., logistic regression, neural networks trained with cross-entropy loss), econometrics, and biological sciences.
Common alternatives include Bayesian methods (which incorporate prior beliefs), the method of moments, and least squares estimation (which is equivalent to MLE under normality assumptions).
Yes, maximum likelihood estimators can be biased, especially in small samples, though they often have good properties like consistency and asymptotic efficiency.
In statistics and probability theory, the method or principle of selecting the parameter values of a model that make the observed data most probable.
Maximum likelihood is usually technical/academic in register.
Maximum likelihood: in British English it is pronounced /ˌmæk.sɪ.məm ˈlaɪk.li.hʊd/, and in American English it is pronounced /ˌmæk.sə.məm ˈlaɪk.li.hʊd/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think of a detective: among all possible suspects (parameter values), they choose the one whose story makes the observed evidence (data) most LIKELY.
Conceptual Metaphor
PARAMETER CHOICE IS PATHFINDING (finding the peak of the likelihood 'mountain').
Practice
Quiz
What does 'maximum likelihood estimation' fundamentally aim to do?