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.
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