What Is the Difference Between “Likelihood” and “Probability”?

Answer: In statistics, “likelihood” refers to the chance of observing data given a particular model or hypothesis, while “probability” represents the chance of an event occurring beforehand.

Likelihood vs Probability: Comparison

Feature	Likelihood	Probability
Definition	The probability of observing data given a specific model or hypothesis.	The measure of the likelihood that an event will occur before it happens.
Application	Used in statistical inference to assess the plausibility of different parameter values given observed data.	Used in probability theory to quantify uncertainty associated with the occurrence of future events.
Directionality	Backward-looking: concerns the probability of past observations given a model.	Forward-looking: concerns the likelihood of future events.
Parameterization	Associated with the likelihood of parameter values given observed data.	Associated with the likelihood of outcomes of random experiments or events.
Interpretation	Interpreted as a measure of support for different parameter values given observed data.	Interpreted as a measure of belief or uncertainty about future events.
Example	In linear regression, the likelihood function measures the probability of observing the given set of data points under the assumption that they are generated from a linear relationship between the variables.	The probability of rolling a six on a fair six-sided die is 1661​ because there is one favorable outcome (rolling a six) out of six equally likely possible outcomes.

In summary, probability quantifies the likelihood of future events, while likelihood quantifies the probability of past observations given a specific model or hypothesis. Understanding the distinction between these concepts is crucial for conducting statistical inference and interpreting the results of statistical analyses accurately.