## Data Science

## Introduction to MCMC, dividing it into its simplest terms

I recently posted an article where I used Bayesian Inference and Markov chain Monte carlo (MCMC) to predict the CL round of 16 winners. There, I attempted to elucidate bayesian statistics in relative depth but I didn’t tell much about MCMC to avoid making it excessively large. The post:

So I made a decision to dedicate a full post to introduce Markov Chain Monte Carlo methods for anyone inquisitive about learning how they work mathematically and once they proof to be useful.

To tackle this post, I’ll adopt the divide-and-conquer strategy: divide the term into its simplest terms and explain them individually to then solve the large picture. So that is what we’ll undergo:

- Monte Carlo methods
- Stochastic processes
- Markov Chain
- MCMC

## Monte Carlo Methods

A Monte Carlo method or simulation is a variety of computational algorithm that consists in using sampling numbers repeatedly to acquire numerical ends in the shape of the likelihood of a variety of results of occurring.

In other words, a Monte Carlo simulation is used to estimate or approximate the possible outcomes or distribution of an uncertain event.

An easy example as an instance that is by rolling two dice and adding their values. We could easily compute the probability of every consequence but we could also use Monte Carlo methods to simulate 5,000 dice-rollings (or more) and get the underlying distribution.

## Stochastic Processes

Wikipedia’s definition is “A stochastic or random process could be defined as a set of random variables that’s indexed by some mathematical set”[1].