The never-repeating digits of `pi` can be approximated by
22/7 = 3. 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!
Curiously, the 22/7 rational approximation of `pi` is more accurate (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! And therefore worth celebrating.
The poster shows the accuracy of 10,000 rational approximations of `pi` for each
m=1..10,000. Read about the details of the method.
Correlation implies association, but not causation. Conversely, causation implies association, but not correlation.
This month, we distinguish between association, correlation and causation.
Association, also called dependence, is a very general relationship: one variable provides information about the other. Correlation, on the other hand, is a specific kind of association: an increasing or decreasing trend. Not all associations are correlations. Moreover, causality can be connected only to association.
We discuss how correlation can be quantified using correlation coefficients (Pearson, Spearman) and show how spurious corrlations can arise in random data as well as very large independent data sets. For example, per capita cheese consumption is correlated with the number of people who died by becoming tangled in bedsheets.
For making probabilistic inferences, a graph is worth a thousand words.
This month we continue with the theme of Bayesian statistics and look at Bayesian networks, which combine network analysis with Bayesian statistics.
In a Bayesian network, nodes represent entities, such as genes, and the influence that one gene has over another is represented by a edge and probability table (or function). Bayes' Theorem is used to calculate the probability of a state for any entity.
In our previous columns about Bayesian statistics, we saw how new information (likelihood) can be incorporated into the probability model (prior) to update our belief of the state of the system (posterior). In the context of a Bayesian network, relationships called conditional dependencies can arise between nodes when information is added to the network. Using a small gene regulation network we show how these dependencies may connect nodes along different paths.
Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayesian Statistics Nature Methods 12:277-278.
Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayes' Theorem Nature Methods 12:277-278.
The Points of Significance column is on vacation this month.
Meanwhile, we're showing you how to manage small multiple plots in the Points of View column Unentangling Complex Plots.
Data in small multiples can vary in range, noise level and trend. Gregor McInerny and myself show you how you can deal with this by cropped and scaling the multiples to a different range to emphasize relative changes while preserving the context of the full data range to show absolute changes.
McInerny, G. & Krzywinski, M. (2015) Points of View: Unentangling complex plots. Nature Methods 12:591.
The Jurassic World Creation Lab webpage shows you how one might create a dinosaur from a sample of DNA. First extract, sequence, assemble and fill in the gaps in the DNA and then incubate in an egg and wait.
With enough time, you'll grow your own brand new dinosaur. Or a stalk of corn ... with more teeth.
What went wrong? Let me explain.
You've seen bound volumes of printouts of the human reference genome. But what if at the Genome Sciences Center we wanted to print everything we sequence today?
I was commissioned by Scientific American to create an information graphic based on Figure 9 in the landmark Nature Integrative analysis of 111 reference human epigenomes paper.
The original figure details the relationships between more than 100 sequenced epigenomes and genetic traits, including disease like Crohn's and Alzheimer's. These relationships were shown as a heatmap in which the epigenome-trait cell depicted the P value associated with tissue-specific H3K4me1 epigenetic modification in regions of the genome associated with the trait.
As much as I distrust network diagrams, in this case this was the right way to show the data. The network was meticulously laid out by hand to draw attention to the layered groups of diseases of traits.
This was my second information graphic for the Graphic Science page. Last year, I illustrated the extent of differences in the gene sequence of humans, Denisovans, chimps and gorillas.