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lunch break
Distractions and amusements, with a sandwich and coffee.
visualization + design
`\pi` Approximation Day Art Posters
The never-repeating digits of `\pi` can be approximated by 22/7 = 3.142857 to within 0.04%. These pages artistically and mathematically explore rational approximations to `\pi`. This 22/7 ratio is celebrated each year on July 22nd. If you like hand waving or back-of-envelope mathematics, this day is for you: `\pi` approximation day!
getting it mostly right
Curiously, the 22/7 rational approximation of `\pi` is more accurate (to within 0.04%) than using the first three digits 3.14, which are accurate to 0.05%.
It seems that `\pi` Approximation Day is 20% more accurate (verify on Wolfram Alpha)! And therefore definitely worth celebrating. $$ \frac{(\pi-3.14)-(22/7-\pi)}{\pi-3.14} = 0.206 $$
art of `\pi` rational approximation
The poster shows the accuracy of 10,000 rational approximations of `\pi` for each `m/n` and `m=1...10000`. Read about the details of the method.
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art of `\pi`-approximate packing
These posters show warped circles, which embody the 22/7 approximation of `\pi`, using a retro 1970's color scheme. Read about the details of the method.
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news + thoughts
Quantile regression
Quantile regression robustly estimates the typical and extreme values of a response.Quantile regression explores the effect of one or more predictors on quantiles of the response. It can answer questions such as "What is the weight of 90% of individuals of a given height?"
Unlike in traditional mean regression methods, no assumptions about the distribution of the response are required, which makes it practical, robust and amenable to skewed distributions.
Quantile regression is also very useful when extremes are interesting or when the response variance varies with the predictors.
Das, K., Krzywinski, M. & Altman, N. (2019) Points of significance: Quantile regression. Nature Methods 16:451–452.
Background reading
Altman, N. & Krzywinski, M. (2015) Points of significance: Simple linear regression. Nature Methods 12:999–1000.
Analyzing outliers: Robust methods to the rescue
Robust regression generates more reliable estimates by detecting and downweighting outliers.Outliers can degrade the fit of linear regression models when the estimation is performed using the ordinary least squares. The impact of outliers can be mitigated with methods that provide robust inference and greater reliability in the presence of anomalous values.
We discuss MM-estimation and show how it can be used to keep your fitting sane and reliable.
Greco, L., Luta, G., Krzywinski, M. & Altman, N. (2019) Points of significance: Analyzing outliers: Robust methods to the rescue. Nature Methods 16:275–276.
Background reading
Altman, N. & Krzywinski, M. (2016) Points of significance: Analyzing outliers: Influential or nuisance. Nature Methods 13:281–282.
Two-level factorial experiments
To find which experimental factors have an effect, simultaneously examine the difference between the high and low levels of each.Two-level factorial experiments, in which all combinations of multiple factor levels are used, efficiently estimate factor effects and detect interactions—desirable statistical qualities that can provide deep insight into a system.
They offer two benefits over the widely used one-factor-at-a-time (OFAT) experiments: efficiency and ability to detect interactions.
Since the number of factor combinations can quickly increase, one approach is to model only some of the factorial effects using empirically-validated assumptions of effect sparsity and effect hierarchy. Effect sparsity tells us that in factorial experiments most of the factorial terms are likely to be unimportant. Effect hierarchy tells us that low-order terms (e.g. main effects) tend to be larger than higher-order terms (e.g. two-factor or three-factor interactions).
Smucker, B., Krzywinski, M. & Altman, N. (2019) Points of significance: Two-level factorial experiments Nature Methods 16:211–212.
Background reading
Krzywinski, M. & Altman, N. (2014) Points of significance: Designing comparative experiments.. Nature Methods 11:597–598.
Happy 2019 `\pi` Day—
Digits, internationally
Celebrate `\pi` Day (March 14th) and set out on an exploration explore accents unknown (to you)!
This year is purely typographical, with something for everyone. Hundreds of digits and hundreds of languages.
A special kids' edition merges math with color and fat fonts.
Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day, 2016 `\pi` Day, 2017 `\pi` Day and 2018 `\pi` Day.
Tree of Emotional Life
One moment you're :) and the next you're :-.
Make sense of it all with my Tree of Emotional life—a hierarchical account of how we feel.
Find and snap to colors in an image
One of my color tools, the colorsnap application snaps colors in an image to a set of reference colors and reports their proportion.
Below is Times Square rendered using the colors of the MTA subway lines.
Colors used by the New York MTA subway lines.
