with Python Code — Why did someone need to invent the Bayesian Inference? In a nutshell, Bayesian inference was invented to update probability as we gather more data. The essence of Bayesian Inference is to combine two different distributions (likelihood and prior) into one “smarter” distribution (posterior). The posterior is considered “smarter” because, unlike classic maximum likelihood estimation (MLE), it takes into account…

with examples and proofs — 1. What is Prior? Prior probability is the likelihood of an event occurring before we see the evidence (data). In Bayesian Inference, the prior is our first estimate of probability based on what we know now, before additional evidence (new data) becomes available. 2. What is Conjugate Prior? Conjugate prior cannot be understood unless one is familiar with Bayesian…

When should you use a Poisson Distribution? — Before we set the parameter λ and plug it into the formula, let’s pause for a second and ponder a few questions. Why did Poisson have to invent the Poisson Distribution? Why does this distribution exist (= why did he invent it)? When is Poisson the appropriate choice for modeling? 1. Why did Poisson invent the Poisson Distribution? …

When should we use the Beta distribution? — The Beta distribution is a probability distribution on probabilities. It is a versatile probability distribution that could be used to model probabilities in different scenarios. Examples include the Click-Through Rate (CTR) of an advertisement, the conversion rate of customers purchasing on your website, the likelihood of readers clapping for your…

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The best way to see if two variables are related — You’ve probably heard of the term “Chi square test” at least once in your life if you have ever studied for the SAT, or worked in some science-related field. Chi-square test is used a lot in corporations, especially when making decisions involving, for instance, medical, product design, engineering, and nearly…

Is your New Year’s resolution to write more math blogs on Medium? Then here is what you need to do to write subscripts, which are pretty essential elements of a math blog, on Medium. I waited for Medium to add this feature, but it just never does, so as of…

Funny, I joined Scale two years ago, but I just wrote this article about why I joined this startup. I’m reposting this from my company’s blog because I think it has some of my strongest feelings about engineering and building in general. Aerin is an engineering manager at Scale AI…