Maximum Likelihood Estimation

The main goal of statistical inference is learning from data. However, data we want to learn from are not always available/easy to handle. Imagine we want to know the average income of American women: it might be unfeasible or highly expensive to collect all American women’s income data. Besides, even in a scenario when this …

Markov Chain Montecarlo

A Markov chain can be defined as a stochastic process Y in which the value at each point at time t depends only on the value at time t-1. It means that the probability for our stochastic process to have state x at time t, given all its past states, is equal to the probability …

Understanding Rejection Sampling method

Rejection sampling is a computational technique whose aim is generating random numbers from a target probability distribution f(x). It is related to the general field of MonteCarlo methods, whose core is generating repeated random sampling to make numerical estimation of unknown parameters. Some words about Randomness One might ask why a random variable with probability …

Convergence of Random Variable

When we talk about convergence of random variable, we want to study the behavior of a sequence of random variables {Xn}=X1, X2,…,Xn,… when n tends towards infinite. Basically, we want to give a meaning to the writing: A sequence of random variables, generally speaking, can converge to either another random variable or a constant. However, …