This article is a summary of a YouTube video "Binomial distributions | Probabilities of probabilities, part 1" by 3Blue1Brown

Choosing the Right Seller Based on Ratings: A Bayesian Approach

TLDRWhen faced with multiple sellers offering the same product at the same price, it can be challenging to decide which one to buy from. This video explores a Bayesian approach to make that decision by analyzing the success rate and reviews of each seller.

Key insights

🤔The more data we see about a seller's ratings, the more confidence it gives us in the rating.

📊We may be suspicious of 100% ratings, as they often come from a small number of reviews.

🎲We can use a binomial distribution to model the situation and calculate the probability of various outcomes.

💡Laplace's rule of succession suggests pretending there were two additional reviews (one positive and one negative) to estimate the true success rate.

📈By comparing the probabilities of positive outcomes for different success rates, we can determine the most likely seller to provide a good experience.

Q&A

How do we make our intuition about ratings quantitative?

We can use a Bayesian approach and probability calculations to quantify our intuition about ratings.

What is Laplace's rule of succession?

Laplace's rule of succession suggests pretending there were two additional reviews (one positive and one negative) to estimate the true success rate.

Why should we be suspicious of 100% ratings?

100% ratings often come from a small number of reviews, making it more plausible that things could have gone differently.

How can we compare sellers' ratings objectively?

By calculating the probabilities of positive outcomes for different success rates using the binomial distribution.

What are some real-world applications of this approach?

This approach can be applied to situations where you need to make judgments about a random process from limited data, such as quality control in manufacturing.

Timestamped Summary

00:00Introduction to the challenge of choosing a seller with multiple offering the same product at the same price.

00:28The instinct to have more data for more confidence in a rating.

01:11Introduction to the Bayesian approach and using the binomial distribution to model the situation.

01:46Explanation of Laplace's rule of succession and how to estimate the true success rate.

02:39Using probabilities of positive outcomes to compare sellers and determine the best bet.

03:00Step 1: Modeling the situation and defining the goal.

05:40Challenge of uncertainty about the true success rate and the probability of seeing the observed data.

08:01Introduction to the binomial distribution and its relevance to random events with two outcomes.

08:23Explanation of how the probability of the data given an assumed success rate relates to the probability of a success rate given the observed data.

10:45Exploration of the probability distribution and finding the center of mass to make judgments about the success rate.