Bayesian Thinking for Non Math People
Let’s start this with a problem. 🧮
Imagine you just met a guy named Steve. You chat with him for a few minutes and notice he doesn’t speak clearly, is extremely shy and won’t look you in the eye.
If you had to guess would you say Steve is more likely to be a math major or a business school major?
Think about it for a second….
If you’re like most people you would have picked math major reasoning that shyness is characteristic in math majors.
There is just one assumption that most people, myself included, forget when looking at this problem.
How many math students are there relative to business school students?
The answer is a lot fewer. Business school students massively outweigh math majors. Let’s just assume it’s a 1/10 ratio from math:business.
We now need to find out how common is shyness in both populations.
Let’s say 70% and 15%.
We can assume Steve is within the shy coherent for each group. From here we just need to multiple the ratios to get our answer… Steve is MUCH more likely to be a business school graduate.
We may assume that Steve is a math student because he’s shy but the fact is there are just MORE shy business students overall making it more likely he’s in the latter group.
** I made this question as simple as possible to help everyone understand**
This is known as the Bayesian Trap or the base rate fallacy.
For you math lovers out there, here is the formula.
The important part to notice here is that we are calculating multiple probabilities, not just one.
The main concept behind this is that information or statistics don’t occur in a vacuum.
A small sample is taken out of a larger one which MUST be understood in order to understand the true prevalence of a given event.
The problem is we rarely think like this.
Linear thinking is seductive and simple causality or “facts” often misled us to not thinking on a second order level.
Let’s do one more.
Let’s say you take a test for a disease, let’s call it dinosaur disease. 🦖🦖
You take the test and oh no … you have dinosaur disease. The doctor tells you it has a 99% accuracy.
What is your chance of having the disease?
Most people say 99%.
The answer is more like 9-10%.
We need to look at the error rate. In this case the error rate is 1%.
If the test is administered to a population of 1000 people that would indicate there would be 10 false positives given a 1% error rate.
1/10 = roughly 9-10%
Here is a good image that visualizes what I’m talking about..
We need to look beyond the initial number and ask additional questions about the sample set.
Results NEED to be understood within a larger context.
Bayesian Thinking in Every Day Life
Bayesian thinking is one of the most powerful laws in probability and statistics.
Learning how this works won’t take long and it will dramatically increase your understanding of how to perceive risk and make better decisions.
If you’re still struggling to understand it, you can think of it as the probability of an event based on prior information or knowledge of conditions that may/may not be related to an event.
This is also commonly known as a conditional probability.
What is the probability that A will happen in relation to B or even C. This can get pretty hairy pretty quickly. We tend to assume that A often occurs in a vacuum with no other variables or numbers affecting it. That definitely isn’t the case.
It’s vital to think of the background information or context that a particular number is framed within.
Without it you’re going to miss out on the big picture. 🖼️
Here are a couple of heuristics when thinking like a Bayesian expert:
- What larger sample is a smaller sample taken from?
- Am I making assumptions when coming to an answer?
- What is the error rate? Most thinkings on the macroscale don’t have a 100% positive rate
- What personal assumptions am I pulling into a decision?
Congrats you just upgraded your cognition. 🧠💪