Happy May 2nd my amazing reader,
You read the title. Some of you are now looking blankly at the screen. Some of you are looking at the screen in terror right now. Almost none of you are giddy about this. And I get that. Bayesian Stats can be very scary.
In my last week’s Math Monday, I covered the Math needed for Computer Science. Over there, I mentioned that you need Bayesian Thinking. This week, I will elaborate upon it, and share some amazing resources for you.
This is a slightly harder topic. I would suggest saving this email/post and coming back to it till you’re very comfortable with the ideas discussed here. Remember, your interview prep is a marathon, not a sprint. There’s no point rushing ahead for one interview and forgetting everything later. You’re much better off developing mastery of the ideas I discuss so that you don’t have to kill yourself preparing again.
Why Bayes Theorem is Important
I don’t want to waste your time talking about the Mathematical significance of the Bayes Theorem. You can find a lot of explanations all over the place.
Instead, I will tell you why you should care about Bayes Theorem. Math is a Language, that allows us to unravel the story of the world. So what part does Bayes Theorem play?
Bayes Theorem allows us to update our beliefs about a particular event based on certain aspects and prior beliefs. Let’s take an example-
90% of the world likes ice-cream.
So you would say the probability of a random person Timmy liking ice cream is (0.9).
Now imagine you find out Timmy doesn’t like sweet things. Chances are Timmy will not like ice cream. The probability of Timmy liking ice cream given that he doesn’t like sweet things is going to be different than 0.9
That in a nutshell is Bayes Theorem. It allows us to come up with Math and quantify situations based on all the evidence we have collected.
If you’re looking to get into Data Science or Deep Learning, your ears are probably ringing with excitement. The rest of you are asking me one thing, What does this have to do with me?
Why Bayesian Thinking is crucial for Software Developers
As software developers, we spend a lot of time designing and implementing systems. Especially, when you become a senior manager, you will have to do large-scale analysis to figure out the kinks of whatever you are developing. To do so, you will have to parse through a lot of information and make your decisions. I’m sure you are confident in your ability to correctly figure out relationships. Do me a solid, and watch the following video by the amazing YouTuber Zach Star.
If you want more mind-bending probability check out the Math Monday about Probability Paradoxes.
This should help you realize something- our minds are terrible with statistics, especially when things involve a Bayesian component. We tend to flip the conditionality, treat priors as final values, and a bunch of other mistakes. And what most people don’t realize is that a lot of the thinking we do is implicitly Bayesian. Not realizing-or not clearly framing situations- that leads to all kinds of fallacies, and can have tragic consequences. Ignore Bayesian Thinking at your own peril.
Learning Bayesian Thinking
Now you’re one of the Woke Few, the next step is how you can work Bayes Theorem into your mind.
We will start with this amazing video by the legendary StatsQuest. When it comes to understanding the intuition behind the Math, there are few people that can match him.
Now that you have watched this video, you’re already 60% of the way through. You should have now a great foundation for imagining how Bayesian Thinking works.
Next up is 3Blue1Brown. He has a beautiful visualization of the Bayes Theorem, that can help you rework your thinking. He’s another amazing YouTuber, who can help you see Math through a novel and amazing lens.
With these two videos, you have already finished 80% of our course. Now for the remaining 20 %.
Refining your Thinking
Now is when we get to the part most people dread. We do the MATH. YAYY!! I can feel your enthusiasm through the screen <3.
Pick up any old textbook and do a few Math Questions involving Bayes Theorem. You don’t need to proceed past the introductory level, since it won’t be useful to most of you. Khan Academy and Brilliant are two amazing websites that I used for myself to gain practice. With this, we only have 5% left.
For my AI nerds, DM me, and I will tell you where you should go from here.
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The last 5% is a lifelong journey. As they say in Sports, use it or lose it. You will get Rusty with Bayesian Stats if you don’t keep thinking in that way. As you proceed with your life, try to spot instances of the Bayes Theorem. You will notice that people often use incorrect Bayesian thinking in their arguments. Learn to catch and frame situations in the Bayesian Context. The good news is that you won’t have to do too much here. Occasional practice will be enough to keep you sharp.
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Happy Prep. I’ll see you at your dream job.
Bayes Theorem is amazing,
Devansh <3
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