Probabilty vs Likelihood
Probability
What is the probability of observing x given the distribution ?
It is the area under the distribution graph.
Distribution is fixed and we want to know the probability of observing data x with that distribution.
예시)
쥐들의 몸무게의 분포를 알고 있는데, 그렇다면 어떤 쥐가 30그람의 몸무게를 가질 확률은 무엇인가?
Likelihood
Data is fixed and we want to know how likely it is to observe data point under some distribution.
We can compare different distributions to find the most likely distribution (aka, a distribution that fits the data the best).
예시)
30그람의 몸무게를 가진 쥐가 있는데, 어떤 분포가 가장 이 쥐의 몸무게를 잘 나타내주는가?