The terms Likelihood and Probability are used interchangeably, but few people know the differences between the two.
In layman's terms, the two terms are interchangeable. The terms "likelihood" and "probability" refer to the likelihood of events occurring. In terms of philosophy, the two words have the same denotative meaning. However, these two terms are used in completely different contexts.
What Are Likelihood and Probability?
Probability is a branch of mathematics that deals with the possibility of a random experiment occurring. The term "probability" refers to the possibility of something happening.
The term Likelihood refers to the process of determining the best data distribution given a specific situation in the data.
When calculating the probability of a given outcome, you assume the model's parameters are reliable.
However, when you calculate the likelihood, you’re attempting to determine whether the parameters in a model can be trusted based on the sample data you have observed.
Now, understand this concept with the help of an example.
Suppose you have an unbiased coin. If you flip the coin, the probability of getting head and a tail is equal, which is 0.5
Now suppose 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. If the coin were fair, it would have shown heads and tails the same number of times.
When calculating the probability of coin getting heads, you assume that P(head) = 0.5
However, when calculating the likelihood, you are trying to find if the model parameter (p = 0.5) is correctly specified or not.
The fact that a coin only lands on heads 14 times out of 50 makes you highly suspicious that the true probability of a coin landing on heads on a given toss is p = 0.5.
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In this tutorial, you learned about the basic difference between Likelihood and Probability. You explored the meaning and the method of interpretation.
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