The definition of a chi-square distribution is given. Chi-square is defined as the sum of random normally distributed variables (mean=0, variance=s.d.=1). The number of added squared variables is equal to the degrees of freedom. With more degrees of freedom the probability of larger chi-square values is increased.

This Perspective argues that ergodicity — a foundational concept in equilibrium statistical physics — is wrongly assumed in much of the quantitative economics literature. By evaluating the extent to which dynamical problems can be replaced by probabilistic ones, many economics puzzles become resolvable in a natural and empirically testable fashion.

This course describes Bayesian statistics in which one s inferences about parameters or hypotheses are updated as evidence accumulates You will learn to use Bayes rule to transform prior probabilities into posterior probabilities and be introduced to the underlying theory and perspective of the Bayesian paradigm The course will apply …

This statistics and data analysis course will introduce you to the essential notions of probability and statistics We will cover techniques in modern data analysis estimation regression and econometrics prediction experimental design randomized control trials and A B testing machine learning and data visualization We will illustrate these concepts with …