It was bad timing to raise money because we didn’t know what we were doing. We didn’t have a product and we didn’t have

on June 1, 2007. Just a month before that, newspapers were relentlessly covering the largest bankruptcy case in the subprime mortgage space. 3,200 people were laid off at a single company, and the spirits of impending doom were taking hold.

I’ll link this excellent overview by Jason Brownlee. Naive Bayes is a very common classification model that calculates P(class|data), or probability of a class given the data. Bayes Optimal Classifier can be used to predict on new observations given previous training data. Bayesian optimization can be used to fine-tune hyperparameters of ML models. Brownlee covers all these and more in the guide, and he does it better than I could.

Given that it’s raining, what is the probability that a casual rider will rent a bike? Given high temperatures, what is the probability of good weather? How does that affect ridership? These questions can be approached in many ways, but hopefully applying Bayes’ theorem will now be an option you consider! Understanding A/B testing, for example, is a great application.

I embraced a makeup detox, regular REM cycles, and renewed interest in cooking that lockdown prescribed. My apartment became the Swiss Army knife of locales: home, gym, office, bar. I learned to find joy in tasks previously categorized as mundane, looked forward to errands like they were adventures, and attempted to reframe all the time alone as self-care.

But by June my tie-dyed sweats began to fade and Zoom happy hours had become a chore. What started as a welcomed vacation from the daily stresses of living a busy, hedonistic life had become a purgatory of monotony. I missed all aspects of regular life but was especially nostalgic for nights out: dressing up, buying overpriced drinks, bonding with strangers in line for the bathroom.

There was an interesting and controversial article released in 2005 by John Ioannidis titled, “Why Most Published Research Findings Are False”. In it, he uses Bayes’ Theorem to argue that, much like in our example above, the probability that a phenomenon is true given a positive research result is much lower than we think. This can be dangerous because we may be taking research as fact without additional verification. It also highlights an important issue in the scientific community, mainly that there is little funding/interest in replicating previous studies.

Let’s start with a classic example in Bayes’ Theorem, getting tested for a rare disease! Here’s our base formula and then we can substitute what we are actually looking for, mainly “What is the probability that you have the disease given that you tested positive?”. If we’ve heard that the test is 95% accurate, then the obvious, intuitive, and incorrect answer is .95!

P(positive|disease) → what is the probability that you had a positive test result given that you do have the disease? This is the test’s sensitivity, or true positive rate, 95% here. And let’s say the test’s specificity, the true negative rate, is also 95%.

Every evening indoors felt more agonizing than the last. I was growing increasingly concerned that my collection of Glossier lipsticks would dry up before I’d have the chance to use them again. If I had known the guy I went on a date with just before lockdown would be the last male contact I’d have for six months, I would have absolutely slept with him… again.

Bayes’ Theorem allows us to overcome our incorrect intuitions about conditional probability in a logical, straightforward manner. Its applications are real and varied, ranging from understanding our test results (with real-world consequences) to improving our machine learning models. I hope this guide was useful and illuminated some of the counterintuitive aspects of Bayes’.

P(positive) → what is the probability of testing positive? This is where the first wrench is introduced because you can test positive and have the disease (the true positives) or you can test positive and not have the disease (the false positives).

As humans, we’re pretty bad at understanding the relative size of numbers especially as the order of magnitude increases. What’s happening here is that we are seeing 95% true positive and not realizing that 95% of a small number is less than 5% of a much larger number! This is what P(pos) is capturing. Given a positive test, you are much more likely to be healthy and receive a false positive than you are to have the disease (it’s only 1/1000 after all) and get a positive test.

Bayes’ can be leveraged to better understand your data. As an example, I’ve been exploring this popular Bike Sharing Ridership dataset. In it we have various features related to weather conditions that you could use to ask interesting questions and drive business understanding.

Because independence means their children’s eventual departure, and departure means loss of control, they will do everything in their power to stop that. They’d rather have their children develop a lifelong dependency than see them succeed on their own.

On a particularly lonely Saturday night, triggered by a friend’s quarantine engagement, I opened my favorite dating app. (This is much like having a favorite dental floss; sure, technically I have a preference, but it in no way makes the task more enjoyable.) I was surprised to see so many profiles updated to include mentions of antibodies and socially distanced dates. While my Instagram feed was evidence enough that millennials were largely ignoring stay-at-home orders, I didn’t assume that necessarily translated into dating. While I doubted their motivations were romantic (were they ever), I was still excited to see so many eligible bachelors within my zip code.

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