What is the Difference Between Likelihood and Probability?

The terms "likelihood" and "probability" are often used interchangeably, but they have different meanings in the context of statistics and data analysis. The main differences between likelihood and probability are:

• Context: Probability is a measure of the chance of occurrence of a particular event, while likelihood is a measure of how well a set of data fits a specific statistical model.
• Parameter Estimation: When calculating the probability of a given outcome, you assume the model's parameters are reliable. However, when calculating the likelihood, you're attempting to determine whether the parameters in a model can be trusted based on the sample.
• Relation to Hypotheses: Probabilities attach to results, while likelihoods attach to hypotheses. In data analysis, the "hypotheses" are often a possible value or a range of possible values for parameters, such as the mean of a distribution.

In summary, probability is used to quantify the chance of an event happening, while likelihood is used to assess the plausibility of different parameters in a statistical model given the observed data. Probability is about a finite set of possible outcomes, while likelihood is about an infinite set of possible probabilities.

Comparative Table: Likelihood vs Probability

The terms "likelihood" and "probability" are often used interchangeably, but they have distinct meanings in the context of statistics. Here is a table highlighting the differences between the two concepts:

To illustrate the difference with an example, consider an unbiased coin. If you flip the coin, the probability of getting heads is 0.5. However, if the same coin is tossed 50 times and it shows heads only 14 times, you would assume that the likelihood of the unbiased coin is very low. In this case, the probability remains 0.5 (assuming the coin is fair), but the likelihood of the coin being fair is low based on the observed data.