Here we are now at the middle of the fourth large part of this talk.
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• get nowhere

One of my goals in life, which I can now say has been accomplished, is to make biology look like astrophysics. Call it my love for the Torino Impact Hazard Scale.

Recently, I was given an opportunity to attend to this (admittedly vague) goal when Linda Chang from Aly Karsan's group approached me with some microscopy photos of mouse veins. I was asked to do "something" with these images for a cover submission to accompany the manuscript.

When people see my covers, sometimes they ask "How did you do that?" Ok, actually they never ask this. But being a scientist, I'm trained me to produce answers *in anticipation* of such questions. So, below, I show you how the image was constructed.

The image was published on the cover of PNAS (PNAS 1 May 2012; 109 (18))

Below are a few of the images I had the option to work with. These are mouse embryonic blood vessels, with a carotid artery shown in the foreground with endothelial cells in green, vascular smooth muscle cells in red and the nuclei in blue.

Of course, as soon as I saw the images, I realized that there was very little that I needed to do to trigger the viewer's imagination. These photos were great!

Immediately I thought of two episodes of Star Trek (original series): Doomsday Machine and the Immunity Syndrome, as well as of images from the Hubble Telescope.

I though it would be pretty easy to make the artery images look all-outer-spacey. They already looked it.

And then I saw the image below.

The background was created from the two images shown here. The second image was sampled three times, at different rotations.

The channel mixer was used to remove the green channel and leave only red and blue.

The next layer was composed of what looked like ribbons of blue gas. This was created by sampling the oval shapes from the source images. Here the red channel was a great source for cloud shapes, and this was the only channel that was kept. The hue was shifted to blue and a curve adjustment was applied to increase the contrast.

When the foreground and middle ground elements were combined, the result was already 40 parsecs away.

The foreground was created from the spectacular comet-like image of a mouse artery. Very little had to be done to make this element look good. It already looked good.

I applied a little blur using Alien Skin's Bokeh 2 to narrow the apparent depth of field, masked out elements at the bottom of the image and removed some of the green channel. The entire blue channel was removed altogether (this gave the tail of the comet a mottled, flame-like appearance).

And here we have the final image.

Building on last month's column about Bayes' Theorem, we introduce Bayesian inference and contrast it to frequentist inference.

Given a hypothesis and a model, the frequentist calculates the probability of different data generated by the model, *P*(data|model). When this probability to obtain the observed data from the model is small (e.g. `alpha` = 0.05), the frequentist rejects the hypothesis.

In contrast, the Bayesian makes direct probability statements about the model by calculating P(model|data). In other words, given the observed data, the probability that the model is correct. With this approach it is possible to relate the probability of different models to identify one that is most compatible with the data.

The Bayesian approach is actually more intuitive. From the frequentist point of view, the probability used to assess the veracity of a hypothesis, P(data|model), commonly referred to as the *P* value, does not help us determine the probability that the model is correct. In fact, the *P* value is commonly misinterpreted as the probability that the hypothesis is right. This is the so-called "prosecutor's fallacy", which confuses the two conditional probabilities *P*(data|model) for *P*(model|data). It is the latter quantity that is more directly useful and calculated by the Bayesian.

Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayes' Theorem *Nature Methods* **12**:277-278.

Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayes' Theorem *Nature Methods* **12**:277-278.

In our first column on Bayesian statistics, we introduce conditional probabilities and Bayes' theorem

*P*(B|A) = *P*(A|B) × *P*(B) / *P*(A)

This relationship between conditional probabilities *P*(B|A) and *P*(A|B) is central in Bayesian statistics. We illustrate how Bayes' theorem can be used to quickly calculate useful probabilities that are more difficult to conceptualize within a frequentist framework.

Using Bayes' theorem, we can incorporate our beliefs and prior experience about a system and update it when data are collected.

Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayes' Theorem *Nature Methods* **12**:277-278.

Oldford, R.W. & Cherry, W.H. Picturing probability: the poverty of Venn diagrams, the richness of eikosograms. (University of Waterloo, 2006)

Celebrate `pi` Day (March 14th) with splitting its digit endlessly. This year I use a treemap approach to encode the digits in the style of Piet Mondrian.

The art has been featured in Ana Swanson's Wonkblog article at the Washington Post—10 Stunning Images Show The Beauty Hidden in `pi`.

I also have art from 2013 `pi` Day and 2014 `pi` Day.

The split plot design originated in agriculture, where applying some factors on a small scale is more difficult than others. For example, it's harder to cost-effectively irrigate a small piece of land than a large one. These differences are also present in biological experiments. For example, temperature and housing conditions are easier to vary for groups of animals than for individuals.

The split plot design is an expansion on the concept of blocking—all split plot designs include at least one randomized complete block design. The split plot design is also useful for cases where one wants to increase the sensitivity in one factor (sub-plot) more than another (whole plot).

Altman, N. & Krzywinski, M. (2015) Points of Significance: Split Plot Design *Nature Methods* **12**:165-166.

1. Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments *Nature Methods* **11**:597-598.

2. Krzywinski, M. & Altman, N. (2014) Points of Significance: Analysis of variance (ANOVA) and blocking *Nature Methods* **11**:699-700.

3. Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication *Nature Methods* **11**:879-880.