probability VS likelihood:
https://zhuanlan.zhihu.com/p/25768606
https://www.psychologicalscience.org/observer/bayes-for-beginners-probability-and-likelihood
To approach MLE today, let’s come from the Bayesian angle, and use Bayes Theorem to frame our question as such:
P(β∣y) = P(y∣β) x P(β) / P(y)
Or, in English:
posterior = likelihood x prior / evidence