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Understanding Maximum Likelihood Estimation (MLE)

What Is It? And What Is It Used For?

Tony Yiu
7 min readMar 7, 2020

The first time I learned MLE, I remember just thinking, “Huh?” It sounded more philosophical and idealistic than practical. But it turns out that MLE is actually quite practical and is a critical component of some widely used data science tools like logistic regression.

Let’s go over how MLE works and how we can use it to estimate the betas of a logistic regression model.

What Is MLE?

At its simplest, MLE is a method for estimating parameters. Every time we fit a statistical or machine learning model, we are estimating parameters. A single variable linear regression has the equation:

Y = B0 + B1*X

Our goal when we fit this model is to estimate the parameters B0 and B1 given our observed values of Y and X. We use Ordinary Least Squares (OLS), not MLE, to fit the linear regression model and estimate B0 and B1. But similar to OLS, MLE is a way to estimate the parameters of a model, given what we observe.

MLE asks the question, “Given the data that we observe (our sample), what are the model parameters that maximize the likelihood of the observed data occurring?”

A Simple Example

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Published in Towards Data Science

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Written by Tony Yiu

Data scientist. Founder Alpha Beta Blog. Doing my best to explain the complex in plain English. Support my writing: https://tonester524.medium.com/membership

Responses (1)

What are your thoughts?

Near the top under A Simple Example, I think it should be .5^10 rather than .5^2.

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