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 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; rather, it is 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 plausible the observed data is under those parameters.
Scaling Likelihoods
- Likelihoods are not constrained between 0 and 1. They can take any non-negative value because the likelihood is often the product of probabilities. When dealing with many observations, this product can become very small or very large.
- Normalising or scaling likelihoods to the 0–1 range would incorrectly suggest that likelihood is a probability, which it is not.
Conclusion
- Scaling likelihood to a 0–1 range can be misleading, as it may incorrectly imply that likelihood is a probability.
- While likelihood and probability are related concepts, they are used in different contexts and have distinct interpretations.