MacKay Minutes 2016/06/30

How did we do on our todo list?

 x $\frac{\sin x}{x}$ -.2 .99335 -.15 .99625 -.10 .99833 -0.5 .99958 0 undefined .05 .99958 .10 .99833 .15 .99625
• Laura
• Create tables of p-values for her report (and add p-values inside the report).
• Produce a set of regressions of the rank-two approximation to Mayflower.
• Start the Recipe of the Week feature (done!)
• Get the final data set together (replace my earliest regressions with the SVD imputed values).
• Steve
• continue thinking about the imputePCA code, which is in the missMDA package. I've installed that package on mathstat (if you try to install a package from RStudio it just does it for your local space). Having put the missMDA package in there, I find only binary code -- so we may not be able to easily swipe the source for imputePCA.

• Chaotic dynamics:
• Butterflies, tornadoes and climate modelling (2008) -- this is a short, nice overview of Lorenz, who had just died.
• Ed Lorenz "introduced the notion of 'empirical orthogonal functions' to atmospheric science...." These are related to PCA, which is of course related to the SVD: the vectors of PCA are empirical -- based on data -- and orthogonal. Assuming that they represent a discretization of a continuous phenomenon, one can think of them as a sample of orthogonal functions, also empirically obtained from the data -- EOFs.
• "What makes Lorenz's work interesting ... is the notion of sensitive dependence on initial conditions." [ael: their emphasis]
• "All of Lorenz's papers were exceptional in their clarity and are well worth tracking down as an example of science writing at its best."
• "But how can climate be predictable if weather is chaotic? The trick lies in the statistics. In those same models that demonstrate the extreme sensitivity to initial conditions, it turns out that the long term means and other moments are stable."
• "Another way of saying it is that for the climate problem, the weather (or the individual trajectory) is the noise. If you are trying to find the common signal that is a signature of a particular forcing then averaging over a number of simulations with different weather works rather well. (There is a long standing quote in science – “one person’s noise is another person’s signal” which is certainly apropos here. Climate modellers don’t average over ensemble members because they think that weather isn’t important, they do it because it gives robust estimates of the signal they are usually looking for.)"
• Selections from Deterministic Nonperiodic Flow (Lorenz, 1963)

Moving forward

• Climate and first appearance: what is our model?
• Do atmospheric temp and precipitation constitute "climate"? How about ocean currents?
• Soil temperature as a function of climate -- we've got a model to start with (Chang, et al.).
• One of our "In the News" items suggests the importance of light (even artificial light).
• Can we use the rank one version of our five favorite species, to reduce noise? We create one new variable from the top five, and follow it through time and space....
• Now Laura is trying the rank-two versions.
• We could use some help shoring up the historical in our paper: the introduction (summary of the 1901 paper), and a look back over some of the others (e.g. 1910, to explain what caused a loss of the data for that year).
Historical predecessor to MacKay?


Such observations would be useful in exciting an interest in natural science among the young, as they would form matter for recording the birthdays of flowers, butterflies, and birds, and with which children may compare their own birthdays and those of their friends* For natural history classes in schools it will supply lists of objects to be sought for on country walks and excursions at the proper seasons, and it will furnish special and appropriate subjects for teachers and lectures to explain at the proper seasons,

In the News

• Night-time light pollution is bringing spring forward by a week: Trees start to produce leaves up to 7.5 days early if bathed in light from street lamps and the knock-on effects mean less food for birds
• For Madison: Fish School Us on Wind Power: Record-efficiency turbine farms are being inspired by sealife.
• The world has the right climate goals — but the wrong ambition levels to achieve them: Stopping warming somewhere between 1.5 and 2 degrees Celsius, according to a recent analysis, would still pose a severe threat to coral reefs and the stability of West Antarctica but might avoid most other grave tipping points in the climate system, such as the collapse of East Antarctic glaciers or wintertime Arctic sea ice.
• Now, in a study in Nature, a large team of researchers reaffirm this troubling conclusion in a sweeping manner, by not only reexamining the individual country pledges — also known as Intended Nationally Determined Contributions, or INDCs — but also conducting a meta-analysis of all the past analyses that have already determined that the Paris pledges fall short. And they, too, find after taking stock of all of this research that the current pledges are likely to leave temperatures at 2.6 to 3.1 degrees Celsius warmer than pre-industrial levels by the year 2100, assuming that the pledges themselves are adopted and only their unconditional parts are realized. [ael: my emphasis]

Todo for next week

• We could use some help shoring up the historical in our paper: the introduction (summary of the 1901 paper), and a look back over some of the others (e.g. 1910, to explain what caused a loss of the data for that year). Takers?
• Andy
• will produce first regressions for FAT versus Soil Temperature
• put FAT model stuff done so far into R
• will check out R code provided by Steve, to see what's different between our imputeSVD and imputePCA
• Laura
• Will produce graphics of the "factors" of the rank-two approximation
• Will try the rank-three regressions
• Will try to incorporate the results into wiki tables
• Will try to get soil reports for Nova Scotia (broadly); Dalhousie University might have some info for us....
• Will flesh out the intro historical stuff (1901 and perhaps discuss 1910 situation)
• Will scan an image or two out of Tufte, and add to the report (as well as a reference in the bibliography).
• Will get us a new Recipe of the Week
• Steve
• will get us his new Mathematica code for imputation, and examples
• will make available code for imputePCA R code.

Recipe of the Week

Did anyone try last week's recipe? I haven't yet...:(

Next meeting

Thursday, 7/7, noon

Steve will be out for the rest of the Month after that; Andy may not be available on the 14th (although I should be able to get free for an hour -- the question in my mind is simply what I can do). Maybe we could talk about climate change for an hour or so -- basic theory. Some of the mathematics.