# A Look Back In Time

The science behind why we can see the history of the universe. (Can also be read here: https://karenacai.com/a-look-back-in-time/)

I recently went on a tour of the incredibly impressive James Webb Space Telescope, which is planned to be deployed into space in 2021 [1]. During my tour, the tour guide mentioned how we would be able to see farther back in time with this telescope. This perplexed me. How can we see the past??

I brought this question up to some physicists that I know, and they gave me a super intuitive explanation that I thought would be fun to share!

In order to understand this phenomena, let’s begin first with unraveling what happens when a thunderstorm occurs. …

# Math You Need to Estimate the Weather, Stocks, Robots, and More!

## Particle Filtering — the Monte-Carlo method used for Bayesian Estimation

This tutorial is two-fold: the first part gives a more gentle introduction about Bayesian estimation, and the second part dives into the specifics of the particle filtering algorithm, which is the Monte Carlo method of performing Bayesian estimation.

# PART 1 — Bayesian Estimation

Have you ever stopped to wonder: how do scientists predict the weather? The weather, among other things, is a really random process that seems like it would be impossible to predict in the future. What mathematical tools allows scientists to do this seemingly impossible task?

Scientists could just use a mathematical model that is derived from the laws of physics (i.e. …