Probability
- The probability of an event represents the chance of that event occurring, and it always lies between 0 and 1. For example, the probability of flipping a fair coin and getting heads is 0.5.
Likelihood
- Likelihood, on the other hand, is related to probability but is used differently in statistics, particularly in the context of likelihood functions and statistical inference.
- Likelihood is not a probability itself but a function of the parameters given observed data. It measures how "likely" it is to observe the given data for different parameter values.
- For example, if you have a set of data and a model with certain parameters, the likelihood tells you how likely the observed data is under those parameters.
Scaling Likelihoods
- Likelihoods are not constrained between 0 and 1. They can take any non-negative value. This is because the likelihood is the product of probabilities, and when dealing with many observations, this product can become a very small or very large number.
- Normalizing or scaling likelihoods between 0 and 1 would incorrectly suggest that the likelihood is a probability, which it is not.
Conclusion
Scaling likelihood to a 0-1 range would be misleading, as it might incorrectly imply that likelihood is a probability. Likelihood and probability are related concepts but are used in different contexts with different interpretations.