Parameter Inference -- Maximum Aposteriori – Towards Data Science – Medium

In the previous post, we discussed the motivation behind Maximum Likelihood Estimate and how to calculate it. We also learned a few tricks about calculating the log likelihood of a function by citing the application of monotonic functions, and how they make the entire process of estimating the critical points of a function much easier as they preserve those critical points. Put the #tails (0) and #heads (2) in the equation of theta_MLE, This result tells us that the probability of next flip being Tails is 0 (i.e., it predicts that no flip is ever gonna turn up Tails the coin is always going to show Heads), and it is glaringly obvious that this is not the case (barring the extreme case where the coin is heavily loaded). Now, this poses a big problem in the Parameter Estimation process because it does not give us the accurate probability of the next flip. We know that even a fair coin has a 25% chance of showing two Heads in a row (0.5 x 0.5 0.25).