### Tag Archives: Probability

## MIT Glimpse (Episode 4)

I was interviewed in November 2015 by Alex Albanese on MIT Glimpse. We discussed Benford’s law, cake cutting, and online optimization. We also discussed how to pick the right toilet, why pi sucks, and why you should watch plenty of Youtube videos!

## Why is π so interesting? Relativity 1

## Ergodic Theory, Brownian Motion, Random Walk, PageRank (Hiking in Modern Math 4/7)

## Shannon’s Information Theory (Trek through Math 5/8)

## Hypothesis Test with Statistics: Get it Right!

Statistician Johnson recently claimed that up to 25% of published scientific experimental results were just wrong! To see why, let's get to the bottom of the scientific method! And it's probably more complicated than you think. In this article, we apply it rigorously to "prove" $\pi=3$. This will highlight the actually mechanism of the scientific method, its limits, and how much messages of experiments are often deformed!

## A Model of Football Games

Back then, I simulated the outcome of the 2006 World Cup, based on a modelling of football games. This article explains this model and presents its results.

## Shannon’s Information Theory

Claude Shannon may be considered one of the most influential person of the 20th Century, as he laid out the foundation of the revolutionary information theory. Yet, unfortunately, he is virtually unknown to the public. This article is a tribute to him. And the best way I've found is to explain some of the brilliant ideas he had.

## Conditional Probabilities: Know what you Learn

Suppose a man has two children, one of them being a boy. What's the probability of the other one being a boy too? This complex question has intrigued thinkers for long until mathematics eventually provided a great framework to better understanding of what's known as conditional probabilities. In this article, we present the ideas through the two-children problem and other fun examples.

## The Essence of Quantum Mechanics

Quantum mechanics is the most accurate and tested scientific theory, Its applications to real life are countless, as all new technologies are based on its principles. Yet, it's also probably the most misunderstood theory, because it constantly contradicts common sense. This article presents the most important features of the theory.

## Bayesian Games: Math Models for Poker

How to better understand Poker and card games in general? Bayesian games provide the right mathematical model just for that! These correspond to games with incomplete information and include probabilistic reasonings.

## Advanced Game Theory Overview

This article gives an overview of recent developments in game theory, including evolutionary game theory, extensive form games, mechanism design, bayesian games and mean field games.

## Probabilistic Algorithms, Probably Better

Probabilities have been proven to be a great tool to understand some features of the world, such as what can happen in a dice game. Applied to programming, it has enabled plenty of amazing algorithms. In this article, we discuss its application to the primality test as well as to face detection. We'll also deal with quantum computers, as well as fundamental computer science open problems P=BPP and NP=BQP.