Waldo, revisited

We've seen the scatterplot and marginal distributions of Waldo's location in a collection of Where's Waldo. These were from Ben Blatt at Slate.com. Now Ronald Olsen has added a plot of the contours of a kernel density estimate of the joint frequency distribution of Waldo's location on the facing pages of the Waldo books. Darker color indicates higher density. Olsen then dynamically computes the optimal search path. Try it out. Can you find Waldo quicker?

Kernel Pinterest

Here is a nice idea for displaying a bit more than summary statistics on the variables included in regression studies. This is from the paper "I Need to Try This!": A Statistical Overview of Pinterest. Pinterest is a pin-board photo sharing website. Among other things, this study models the number of re-pins of a given photo with a Negative-Binomial regression.

The table above shows the medians, means, and maxima for non-negative count data included in the regressions. The minima are all zero. Along with these summary statistics are small thumb-nail kernel density estimates of the distributions of the variables. Now granted the variables involved take on only integer values and these distribution curves are continuous, but it is much better than the usual limited summary statistics, shown below, that are often given in other regression studies.

Garage Dings

One-car garages can be very small. Here is the driver's side wall of one such garage (thanks Laura). It displays the dings from opening the driver's side door in the tight space. Of course, the car is not parked in the same spot every time. Sometimes it rests a little farther forward in the garage and the door hits the wall more to the right in this image. Sometimes the car is parked just inside of the garage and the door dings fall on the left of this image. Most often the car is parked more centrally in the garage, leaving a greater frequency of door dings in the middle of the wall. This is a common pattern  on this blog: little wear on the left, much more in the middle, and then little wear on the right. This is the typical pattern of a bell-shaped, symmetric normal distribution, although any unimodal even roughly symmetric distribution could be described similarly.

Perhaps the wall needs a little tweak along these lines:

These are plots that highlight, with color, the highest density regions of a measurement, like the location of the door dings. The densities are estimated by the smooth curves. The measurements are shown by their random arrangement of tickmarks on the horizontal axes below the density curves - just like the garage door dings. These are the plots from Hyndman, R.J. (1996) "Computing and graphing highest density regions" American Statistician, 50, 120-126. These plots are one of many featured graphics in the R graph gallery.

Laura needs some blue, red, and green tape!

Earthquake/Population Density Map

A map of global earthquake intensity, showing magnitude and density of seismic activity weighted by population (larger version here). According to Views of the World this map allows us "to understand the earthquake intensity in relation to today’s population distribution, and thus gives an idea of where most people are of risk related to seismic activity." The algorithm uses kernel density estimation followed by a density equalizing algorithm.
Via The Map Room.

The Density of Space Trash

Here is an image showing the density of space debris in low earth orbit. Notice that this density has a very long, and likely heavy, tail that is not shown. Geo-synchronous satellites orbit at 36,000km well off the upper range of this graph (2,000km). There would be a large bump in the density at 36,000km. From The Washington Post.

Two Colorful Examples of Smoothed Bivariate Density Functions

Seen this week, smoothed scatterplots showing the density of locations of basketball shots taken by Phoenix Suns players. More information is here. Via the Statistical Modeling blog of the Stat Department at Columbia University.

Also this week:

Smoothed scatterplots showing where subjects first looked in recognizing faces. The nose knows. More here.