Decision Mechanics

Insight. Applied.

Statistical intuition

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splash

The Monty Hall problem is a probability puzzle based on an old US game show. You are shown three doors. One contains a car, while the other two contains goats. The game show host invites you to pick a door. He then opens one of the doors containing a goat and asks, "Do you want to stick with your original selection or switch to the remaining door?"

What should you do…assuming that you don’t wish to own a goat?

I’ll take all the fun out of it. You should switch. It doubles your chances of getting the car.

Convinced? Probably not. Even when presented with the solution, many people struggle to accept it. It’s not particularly intuitive.

Martin Johnsson recently discussed this on his blog. He used paper simulation, computer modelling and mathematics to try and satisfy himself of the wisdom of switching. He concluded

…I’m not sure I have convinced myself of the solution to the generalised problem yet.

Reasoning about probabilities is hard. It’s very easy to be led astray by our "gut". As the eminent statistician Sir David Spiegelhalter has noted

…when asked a basic school question using probability, I have to […] try it a few different ways, and finally announce what I hope is the correct answer.

This dereliction of our instincts means that it’s essential to draw on the formal methods of statistics and Monte Carlo simulation when making important decisions.

Photo by Sergiu Vălenaș on Unsplash

R now has native pipes

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The latest release of R introduces an F#-style pipe operator.

Pipes have been available in R for a while, via the magrittr package. However, with the release of R 4.1.0, pipes are supported in base R.

The syntax has changed from that used in magrittr. The magrittr pipe operator is %>%. The new base R pipe operator is |>.

So, instead of

df %>% head()

we have

df |> head()

R 4.1.0 also introduces a lightweight, lambda-style function syntax, which can be usefully combined with the new pipe operator when piping to an argument other than the first one.

iris |> {\(x) lm(Sepal.Width ~ Sepal.Length, data = x)}()

Why is everything so complicated?

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Ever expressed frustration that stuff is unnecessarily complicated? If so, a new paper published in Nature might have an explanation.

Apparently, when solving problems, we have a natural inclination to add things. For instance, when asked to make a design symmetrical, people are more likely to do so by adding features, rather than removing them.

You can see evidence of this in a range of technical domains.

  • UX designers add more cues to address usability issues when they should make the the design less "noisy".

  • Software developers add more code to fix problems instead of simplifying existing code.

  • Data scientists chase R-squared improvements by adding more features.

Simplification is a crucial component of effective decision science. Approaches such as confrontation analysis strip away extraneous details and focus your attention on your immediate dilemmas.

It’s not all doom and gloom. You can "nudge" people to simplify using appropriate cues. For instance, maybe you could display prominent "lines of code" counts, or focus on predictive R-squared when modelling.

Given our instinctive biases we must be vigilant in the search for creeping complexity. Science is showing us that it’s more work to keep it simple.

As President Woodrow Wilson explained,

If I am to speak ten minutes, I need a week for preparation; if fifteen minutes, three days; if half an hour, two days; if an hour, I am ready now.

Photo by Gayatri Malhotra on Unsplash

The company you keep…

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weird combination

Researchers have demonstrated how objects can be hidden by exploiting correlation bias.

Computer vision systems, like other machine learning technologies, rely on correlation and context. They learn that certain things often appear together–like mice and keyboards. But you don’t expect to see a platypus wielding a chainsaw, for example (…you’ve no idea how much I wanted to find that splash image…).

Artwork can be challenging, for example, as it can depict items that have no business being in the wider context.

This opens up another angle for hacking AI systems. The researchers were able to make a computer vision system fail to recognise a STOP sign by placing it next to fruit—a suitably bizarre combination.

Another example of the brittleness of "intelligence as correlation". The state-of-the-art in machine learning is leading us down the latest AI blind-alley. This one may be a little darker than before.

Photo by celery soup on Unsplash.