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Why Statisticians Avoid the Express Lane

Will Kurt

Statistical analysis of why it is possibly preferable to choose

a regular lane over the “express” lane when certain

conditions apply, given that the assumptions of our model

hold.

Who am I?

Data Scientist at Quick Sprout

Blog at CountBayesie.com

Author Learn Haskell (https://www.manning.com/books/learn-haskell)

Factors we need to consider?

Number of People in each line (known/observable)

Number of Items

Time per item

Time per person

Key issue:

Time per person >> Time per item

How do we Choose which is best?

Solution for optimal lane choosing:

Express items = [1 .. 15]

Regular items = [10 .. 60]

People Time Distribution

vs

Let’s explore multiple-universes...

...with Monte-Carlo simulations!!!

Express = 6 Regular = 3

10,000 samples! What’s the probability Regular is faster?

5 v 3 P(Regular faster) = 0.736 v 3 P(Regular faster) = 0.92

Cost of 6 express vs 3 regular

CDF = Best Plot of All time!!!

“But your model is dumb, and I don’t like it.”

Your alternative model...

If people in the express lane is double the number in the regular line then…

P(regular is faster) = 0.99

Otherwise

P(express is faster) = 0.99

Comparing hypotheses with theLikelihood ratio

Ratio: 0.63Your model explains the data ~1.6x better!

Feeling Smart?

Your Model...

Vs.

A Coin Flip!

A coin explains the data 3.2x better than your model!

What did we learn today?

Nothing!

What did we learn today?

Nothing!

Basically all of Statistical Inference (or at least the important bits)

What did we learn today?

Nothing!

Basically all of Statistical Inference (or at least the important bits)

Everything is hard

What did we learn today?

Nothing!

Basically all of Statistical Inference (or at least the important bits)

Everything is hard

We can compare our misunderstanding of the world with the relative strength of our hypotheses

Thank you!!!

Email me at wckurt@gmail.com

Follow me on Twitter @willkurt

Read about probability: https://www.countbayesie.com

Preorder my book on a totally unrelated topic: https://www.manning.com/books/learn-haskell