the meaning of likelihood in maximum likelihood estimation

To my understanding, likelihood has no meaning per se. Only by comparing likelihoods do they become intepretable. Likelihood is unbounded and probability is bounded.

In maximum likelihood estimation, we have likelihood as the function of some parameter value give the data. Here the parameter is not a random variable. It is what we are optimizing. Howerver, maximum likelihood estimation procedure generates a likelihood function that range from 0 to 1. The log-likelihood is therefore from -infinity to 0. Here, the likelihood is bounded (0,1)?

I'm always confused about 'likelihood'. Is the 'likelihood' in maximum likelihood estimation a 'true likelihood'? Can someone help to clarify the concept? Very much appreciated!

• "a likelihood function that range from 0 to 1." Likelihood is similar to probability density function, so it > 0, but can be >1. – user158565 Oct 12 '18 at 18:12
• It basically means your regression line has the maximum likelihood of being the best fitting line to your data. – Kreitz Gigs Oct 12 '18 at 18:13
• Yes, likelihood function in maximum likelihood estimation is a true likelihood. For "What is likelihood?", see stats.stackexchange.com/questions/112451/… – kjetil b halvorsen Oct 12 '18 at 19:24