# Taking A Random Walk

2017-12-12

I was sitting in a bagel shop on Saturday with my 9 year old daughter. We had brought along hexagonal graph paper and a six sided die. We decided that we would choose a hexagon in the middle of the page and then roll the die to determine a direction:

1 up (North)
2 diagonal to the upper right (Northeast)
3 diagonal to the lower right (Southeast)
4 down (South)
5 diagonal to the lower left (Southwest)
6 diagonal to the upper left (Northwest)

Our first roll was a six so we drew a line to the hexagon northwest of where we started. That was the first “step.”

After a few rolls we found ourselves coming back along a path we had gone down before. We decided to draw a second line close to the first in those cases.

We did this about 50 times. The results are pictured above, along with kid hands for scale.

Last Monday we celebrated a “Scientific Marathon” at Royal Botanic Garden in Madrid, a kind of mini-conference to talk about our research. I was talking about the relation between fungal spore size and environmental variables such as temperature and precipitation. To make my presentation more friendly, I created a GIF to explain the Brownian Motion model. In evolutionary biology, we can use this model to simulate the random variation of a continuous trait through time. Under this model, we can notice how closer species tend to maintain closer trait values due to shared evolutionary history. You have a lot of information about Brownian Motion models in evolutionary biology everywhere!

Another place that this is useful is in describing stock market movements in the short run.

## The Lesser-Known Apply Functions In R

2018-11-14

Andrew Treadway covers a few of the lesser-known apply functions in R: rapply Let’s start with rapply. This function has a couple of different purposes. One is to recursively apply a function to a list. We’ll get to that in a moment. The other use of rapply is to a apply a function to only those elements in […]

## Bias Correction In Standard Deviation Estimates

2018-11-13

John Mount explains how to perform bias correction and explains why it happens so rarely in practice: The bias in question is falling off at a rate of 1/n (where n is our sample size). So the bias issue loses what little gravity it ever may have ever had when working with big data. Most sources of noise will […]