In this post, I will show you THE most important technique in inferential statistics: Maximum Likelihood Estimation (MLE).  1. Some data to work with Before we get started, let’s see what type of problem could be solved using MLE. For example, I record the number of visitors of this website each hour from 8:00 am - 12:00 am (p.s. off course this is fake data, and I am probably too optimistic).

Here I am going to show you how to calculate PCA by hand! But before we dive deep into PCA, there are two prerequisite concepts we need to understand: Variance/Covariance Find eigenvectors and eigenvalues If you already understand those two concepts, you can skip this part.  Prerequisite 1: Variance/Covariance Variance Variance measures how far a set of numbers is spread out from their average value. The sample variance is defined as $$ s^2 = \frac{\sum(x_i - \bar x)^2}{n - 1} $$