## … well suited for the early 19th century.

The New York Times reports today that the United States Supreme Court

… late Wednesday night barred restrictions on religious services in New York that Gov. Andrew M. Cuomo had imposed to combat the coronavirus.

The vote was 5 to 4, with Chief Justice John G. Roberts Jr. and the court’s three liberal members in dissent. The order was the first in which the court’s newest member, Justice Amy Coney Barrett, played a decisive role.

Accordingly, both because of this decision, and decisions of the federal judiciary with respect to Juliana vs United States, I’ve concluded that the U.S. Constitution is well-suited for the early 19th century, and even the late 18th, but has no ability to deal with important 21st century problems.

And if anything underscores this it is that the U.S. Constitution leaves the composition, length of tenure, size, and qualifications of justices to the U.S. Supreme Court entirely within the hands of Congress. Moreover, it has an amending mechanism, one which hobbled and slowed with ponderous and maladroit criteria of process and agreement.

And, more than ever, this demonstrates now critical it is for a modern country to utterly and fundamentally sever its governance and discourse from considerations of religion. As noted by Professor Christian Robert at his blog, Xi’an’s Og, a model for government that purports to be universalist must necessarily be secularist. Otherwise there is preference and, so, some religions and religious views are more preferred and acceptable than others, simply because of tyranny of the minority in a society which gives individuals too much power. This inflicts upon society a gross social and policy price of anarchy.

## Codium fragile for Saturday, 21st November 2020

Great Web sites here, all about truly preserving Walpole for the long term, rather than in pursuit of myopic interests:

Choices.

## “Climate Hope” from Climate Adam

 Rainmaker, a little faith for hire Rainmaker, the house is on fire Rainmaker, take everything you have Sometimes folks need to believe in something so bad, so bad, so bad They'll hire a rainmaker

 

Springsteen, 2020 

## Selfish Routing is Why, in the Long Term, CDNs are not in everyone’s best interest

It’s all about the Price of Anarchy, and its implications for routing on the Internet.

These are not only greedy measures, they are monopolistic. And they support oligopoly.

## Choices.

This is a retake of a presentation at the invitation of the Walpole Greens and made at their meeting of 9th November 2020. It is longer and more leisurely. I interleave some of the answers to questions that followed the presentation in the presentation and the remainder, as best as I could remember, are answered at the end. Some of the answers given here are better than the answers I gave on Monday, the 9th, because I was able to look up more about the answers. For instance, there was a question about effects of climate change on PV array output. I answered it, but my answer at the presentation was not crisp.

This concerns a proposal by Norfolk County, Massachusetts to build a 6 MW solar array with two parts on Norfolk County land. There is a Commissioners’ meeting scheduled for the 19th of November to discuss the matter. There is opposition.

The slides are available below:

Choices–JGalkowski–FinalCutForMonday9Nov–20201108

The notes for the slides are available below:

Choices–ShortNotes–JanGalkowski20201108

There is a related report, produced by the Coalition for Community Solar Access, which is available below:

ShiningLightOnMassachusettsSolarLandUseTrends–Hering–Lord–2019

## Complexity vs Simplicity in Geophysics

Really interesting mechanistic reductionism illustrating what it means to explain phenomena scientifically. It’s all about the maths.

In our book Mathematical GeoEnergy, several geophysical processes are modeled — from conventional tides to ENSO. Each model fits the data applying a concise physics-derived algorithm — the key being the algorithm’s conciseness but not necessarily subjective intuitiveness.

I’ve followed Gell-Mann’s work on complexity over the years and so will try applying his qualitative effective complexity approach to characterize the simplicity of the geophysics models described in the book and on this blog.

Here’s a breakdown from least complex to most complex

1. Say we are doing tidal analysis by fitting a model to a historical sea-level height (SLH) tidal gauge time-series. That’s essentially an effective complexity of1because it just involves fitting amplitudes and phases from known lunisolar sinusoidal tidal cycles.

This image has been resized to fit in the page…

View original post 1,040 more words

## Six Principle Plays in Denialist Playbook

It’s all about advancing anti-science and doubts about science, as well as confusing the public for ideological and financial gain.

## Rethinking Environmentalism

Stewart Brand at the Perimeter Institute. Sponsored by KPMG.

## “The bamboozle has captured us.”

“One of the saddest lessons of history is this: If we’ve been bamboozled long enough, we tend to reject any evidence of the bamboozle. We’re no longer interested in finding out the truth. The bamboozle has captured us. It’s simply too painful to acknowledge, even to ourselves, that we’ve been taken. Once you give a charlatan power over you, you almost never get it back.”

## It’s time.

Posted in zero carbon | 2 Comments

## Phase Plane plots of COVID-19 deaths with uncertainties

### I. Introduction.

It’s time to fulfill the promise made in “Phase plane plots of COVID-19 deaths“, a blog post from 2nd May 2020, and produce the same with uncertainty clouds about the functional trajectories(*). To begin, here are some assumptions I’ve made:

• The data in a death series are dependent. So, as in autoregressive models, the current prediction of number of deaths is dependent upon the previous number of deaths, so $y_{t} = f(y_{t-1}, y_{t-2}, \dots, y_{t-\ell})$.
• There is “noise” in observations, and possibly in estimates of deaths. This can be due to a large number of different policies being adopted for when deaths are reported, or it can be because deaths are not being reported at the time they actually occurred, but later. This is typically managed by smoothing of some kind and this analysis, like many others, is no different. Here, however, I’ll be using smoothing splines and, in particular, penalized smoothing splines.
• The noise variability may be heteroscedastic, meaning that there’s no reason to believe the variability at time $t$ is the same as variability at time $t+\delta$, even if $|\delta| = 1$. I’m planning to assume homoscedasticity in one part of the analysis, and then I’ll assume heteroscedasticity in another.
• The best estimate of actual deaths is obtainable through the data, even if the best estimate may be latent and need to be estimated after filtering. I do not use data that count excess deaths, as a rule. However, there may be some county or state included in the data which has included assumed deaths due to COVID-19.
• The estimator for the number of deaths ought, too, to estimate the rate of change in number of deaths, and the acceleration, or rate of change in rate of change in number of deaths at the same time.
• The estimator for the number of deaths and its first two derivatives ought to account for the observations being counts, not continuous measures. While the biggest series counts are quite large, they are still counts, not continuous measures. Nevertheless, robust analysis of such series generally means centering and scaling the series, so, while its shape is preserved, it looks, for all appearances as if it actually is a continuous measure. I treat these as such. If these are to brought back to the original context, this can be achieved by reversing the transformation.

Setting aside the peek ahead to smoothing splines for a moment, a standard approach to dealing with these kind of data is dynamic linear modeling, otherwise known as state-space models. It also suggests using software to estimate the time-varying magnitude of noises, and then extracting that to form the uncertainties in rates and rates of change in rates.

What does that mean, precisely? And is this standard approach the best approach or even a good approach? And how should that be judged?

Let $\hat{y}_{t}$ be the centered and scaled counterpart to a COVID-19 quantity of interest for a specific region (country, state, etc) at time $t$. I’ll assume times come in integer increments, that is, that the reports are uniformly spaced. I’m proposing dynamic linear model or state space model of this as

$\hat{y}_{t} = \left[\begin{array}{c}1 \\ 0 \\ 0 \end{array}\right] \mathbf{x}_{t} + \mathbf{\mathcal{N}}(0, \sigma_{y}^{2})$

$\mathbf{x}_{t+1} = \left[\begin{array}{ccc}1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 0 \end{array}\right] \mathbf{x}_{t} + \mathbf{\mathcal{N}}(\mathbf{0}_{3}, \boldsymbol\Sigma_{\mathbf{x}})$

Here $\mathbf{\mathcal{N}}(\mathbf{0}_{3}, \boldsymbol\Sigma_{\mathbf{x}})$ means a zero mean trivariate Gaussian having a 3-by-3 covariance matrix $\boldsymbol\Sigma_{\mathbf{x}}$.

Expanding the definition of $\mathbf{x}_{t}$, the expression above becomes

$\left[\begin{array}{c} x_{t+1} \\ \dot{x}_{t+1} \\ \ddot{x}_{t+1} \end{array} \right] = \left[\begin{array}{ccc}1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 0 \end{array}\right] \left[\begin{array}{c} x_{t} \\ \dot{x}_{t} \\ \ddot{x}_{t} \end{array} \right] + \mathbf{\mathcal{N}}(\mathbf{0}_{3}, \boldsymbol\Sigma_{\mathbf{x}})$

The idea is to estimate the state components $x_{t}$, $\dot{x}_{t}$, $\ddot{x}_{t}$, and their variances for each $t$.

I used this approach in previous work. Unfortunately, good prediction intervals are not available using the dlm package. It does have a $\text{dlmForecast}$ function, one that’s being developed, but that does not yet offer prediction intervals. Moreover, prediction intervals are not easy to estimate unless errors are distributed as Gaussians(**). These functional data and estimates of their derivatives are not. As that is the primary point of this paper, extending my earlier work, that is a roadblock(***).

As another qualification or criticism, note it is difficult to deal with heteroscedasticity with such a model. Typically, estimates of errors in measurement need to be made independently and fed in as inputs.

So, instead of this approach, I’ve turned to a non-parametric, non-mechanistic way of estimating the latent curve of deaths and the first two derivatives needed to describe the series in the phase plane: Using penalized splines as before, but generalized to techniques which estimate uncertainties in them, whether they are used to spline signal or its derivatives. Specifically, I’m calculating prediction intervals for fits and for derivatives. The primary tool is the bootstrap technique for developing non-parametric prediction intervals, one described in section 3.1 of Denham’s paper:

M. C. Denham, "Prediction intervals in partial least squares", (1997), Journal of Chemometrics, 11(1), 39-52.

Actually, a later paper by Denham,

M. C. Denham, "Choosing the number of factors in partial least squares regression: estimating and minimizing the mean squared error of prediction", (2000), Journal of Chemometrics, 14(4), 351-361.

reveals the idea is from Efron and Tirshirani,

B. Efron, R. J. Tibshirani, An Introduction to the Bootstrap, 1993, Chapman & Hall, problem 25.8, 390-391.

That algorithm is also described in the documentation for the $\text{fplsr}$ function in the R ftsa package, in its subsection titled “Nonparametric method”. This algorithm is used to generate msets of simulated points, one set corresponding to each point in the time series. Actual prediction intervals are calculated from each of these using the $\text{predIntNpar}$ function from the R EnvStats package.

Also, as before, spline regression models and their predictions are done using the R pspline package.

### II. Estimating uncertainties.

Prediction intervals are estimated by bootstrapping residuals, generating predictions from a baseline perturbed prediction, and then using the non-parametric technique for estimating prediction intervals for each point in a time series. That is, and specifically,

1. Fit a smoothing spline to the entire time series, $\mathring{y}_{k}$, one having a length $n$. Use generalized cross validation to estimate the smoothing parameter. Obtain a predicted smoothed series $\mathcal{P}_{k}$ from this spline regression.
2. Calculate residuals $r_{k} = \mathring{y}_{k} - \mathcal{P}_{k}$.
3. Repeating through step 5 $R = 1000$ times, bootstrap $r_{k}$ obtaining $n$ offsets. That is, draw from $\{r_{k}\}$ $n$ values with replacement. Call these $\eta_{k}$.
4. Calculate $S_{k} = \mathcal{P}_{k} + \eta_{k}$.
5. Fit a smoothing spline to $S_{k}$ and predict $\hat{\mathcal{P}}_{j,k}$ for the $j\text{\textit{th}}$ time this is done.
6. For each $k$, over all $j$ instances of bootstrapped predictions, use non-parametric estimation of a prediction interval for time point $k$, considering the slice $\hat{\mathcal{P}}_{.,k}$.

Since observational data on first and second derivatives are not available as given, the companion series of first and second derivatives are obtained by simple differencing and then applying a smoothing spline to those. The same procedure is used to obtained prediction intervals on first and second derivatives, substituting $\dot{y}_{k}$ or $\ddot{y}_{k}$ for $\mathring{y}_{k}$ in the above.

### III. Where the code lives.

The code and datasets used to produce these figures resides in this Google Drive folder.

### IV. How to Display Uncertainties.

After experimenting, I decided that phase plane plots having variable widths or decorations along the trace would be the best way to convey uncertainty. The key observation is that uncertainty in one of the dimensions can be numerically much larger than the other, and that the plot’s aspect ratio can distort these relationships. I decided that an error bar attached to the trace or path indicated by the data would be appropriate, with the bar having an orientation which was consistent with the implied slope of the vertical error over the horizontal error, and a length proportional to the length of their vectorial sum. Also, for reasons of symmetry, such bars would extend both above and below the path having these errors.

I examined using variable-width lines as a part of preliminary experiments. These are in fact supported by base R, but their application is not at all obvious. I did not want my code here to burden readers with mastering grid or ggplot2. I also examined the possibility of using TikZ via tikzDevice. In fact, TikZ can do this:

(Hat tip to matheburg.)

The corresponding code is:

 \documentclass{article} \usepackage{pgfplots} \begin{document} \begin{tikzpicture}[scale=2.5] \begin{axis}[width=7cm, height=7cm, xmin=-1.05, xmax=1.05, axis lines=none, view={0}{25}] \foreach \x in {0,0.5,...,12.0} {\edef\temp{\noexpand\addplot3[blue, line width=1+\x/2 pt, domain=\x:\x+0.5,samples y=0] ( { cos( deg(x) ) }, { sin( deg(x) ) }, { x } ); } \temp } \draw[>=latex,->] (105,100,10) -- (105,100,180); \node at (95,90,178) { $z$ }; \end{axis} \end{tikzpicture} \end{document} 

But, again, do I want people to master TikZ?

Accordingly I chose to keep within R, and devise a means of portraying these uncertainties using its plotting facilities. The decision was ultimately based upon the need to depict both vertical and horizontal errors at the same time, something which simply varying a line width could not portray.

### V. Examples of Phase Plane Plots for COVID-19 Deaths.

I chose to depict uncertainties as ellipses with axes parallel to the two axes in question. So, for instance, if a plot of rate of deaths versus counts of deaths is shown, the horizontal span of the ellipse corresponds to the x-axis rate of deaths prediction interval, and the vertical corresponds to the uncertainty in the number of deaths. Consider, for example, that plot for New York State in the period of study, 13th March 2020 through 16th May 2020:

In all these instances simply click on the image to see a larger version … It’ll pop out into a separate window tab in your browser.

The count of deaths is monotonic so the trend is upwards, and this plot shows the variation in rates of death. Here’s the cumulative deaths over time for the same period:

Note that this kind of trend is pretty universal, so won’t be shown for many of the examples. It is logistic-like, not really exponential. Note that in this case — and in some of the others — there’s an anomaly on the 16th, with rates and counts being zero. This is probably due to incomplete counting on the 16th but could be for other reasons. It actually appears in the data.

Finally, for New York State, here’s the phase-plane plot sought:

The uncertainty envelopes in all cases, whether phase plane or counts versus rates are taken as the 0.667 prediction interval.

There are similar results from Massachusetts:

What’s gratifying is that the phase plane behavior appears real based upon the prediction uncertainties. As will be shown later, this isn’t always the case. Why there might be differences will be discussed in the summary.

Here’s the count versus rates for the United States as a whole:

And it’s phase plane plot also shows separation of the orbits:

although it’s not as clean as for Massachusetts or New York State.

Showing a case where the separation is not at all clear, consider the phase plane plot for Florida:

Apparently the rates for Florida vary widely:

Tennessee provides an intermediate case in its phase-plane plot:

Moving on to other countries, some of the data were quirky at best. There was something about China’s reporting, for instance, that causes singularities in the smoothing spline model builder. I did not investigate, since I’m less interested in any particular country and, one, what patterns reveal overall, and, two, how well these prediction interval methods for phase plane depictions work.

Here’s the phase plane for Switzerland:

Note it suffers an anomaly in the reporting for 16th May 2020 as did New York State.

The counts versus rates for Switzerland is:

Finally, here is the UK’s death counts versus rates of deaths:

### VI. Summary.

Phase plane plots with prediction intervals were successfully constructed based upon death counts data from COVID-19 for several U.S. states and a number of countries. Some of the prediction intervals, such as those for Florida, are large and offer doubt regarding the meaning and interpretation of the phase plane depictions of rates of deaths and accelerations. But some states have reasonable prediction intervals.

It’s interesting to speculate why the differences. It’s possible there was inconsistency in reporting rates, so these mask the variation in the underlying deaths due to disease. If so, that would suggest wide prediction intervals may be an index of data from specific sources being poorly compiled, and so might provide a way of weighting them when being used for other studies. Certainly the consistency with which deaths were reported from New York State and Massachusetts allowed more confidence to be had in the reality of the phase plane orbits. Indeed, with that, these suggest the health governance of these states were tracking cases and taking measures, resulting in deaths and their rates exhibiting control system-like limit cycles.

It’s also interesting that this exercise took a great deal of effort and time, with about a dozen different means of estimating prediction intervals being tried, most in futility. I say “futility” not because prediction interval estimates were not produced but that, even in the cases of New York State and Massachusetts they were so wide to suggest the phase plane plots were meaningless. I was disappointed when split conformal inference prediction via its function $\text{conformal.pred.split}$ did poorly:

J. Lei, M. G’Sell, A. Rinaldo, R. J. Tibshirani, and Larry Wasserman, "Distribution-free predictive inference for regression", Journal of the American Statistical Association 113(523) (2018): 1094-1111.

G. Shafer, Glenn, V. Vovk, "A tutorial on conformal prediction", Journal of Machine Learning Research 9, March (2008): 371-421.

This may be because these time series data are just hard with which to deal, with many blemishes. However, there’s a caution there, because non-parametric means like conformal predictive inference, while they may give up statistical power, are in turn supposed to be robust against such blemishes.

In the end, phase planes and notions from dynamical systems and functional data analysis continue to be useful concepts and offer analytical tools for dealing with important data sets. It was great to see the venerable smoothing spline come out ahead of many other techniques, including some statistical learning approaches.

## “We will love science and its controversies.”

### We will continue, Professor. With all the teachers and professors in France, we will teach history, its glories and its vicissitudes. We will introduce literature, music, all works of soul and spirit. We will love with all our strength the debate, the reasonable arguments, the kind persuasions. We will love science and its controversies. Like you, we will cultivate tolerance. Like you, we will seek to understand, relentlessly, and to understand even more what we would like to move away from us. We will learn humor, distance. We will recall that our freedoms hold only through the end of hatred and violence, through respect for others.

Emmanuel Macron, President of France, at the memorial and funeral of Samuel Paty, the Sorbonne, France.

## “No, COVID-19 Is not the Flu”

Q&A with Andrew Pekosz, PhD, Johns Hopkins University:

## dead bodies vs economic integrity

From The Financial Times.

## “A Matter of Degrees”

A Matter of Degrees” is a new climate change mitigation podcast, created and produced by Drs Katharine Wilkinson and Leah Stokes.

The first episode, “Give up your climate guilt“, is auspicious.

Check it out.

Fair disclosure: I have been pretty negative about Project Drawdown of which Dr Wilkinson was and is a major participant. I specifically don’t buy the afforestation take, and I believe a lot of research has come out since describing and documentation those limits.

## Tesla 3 to Ithaca, NY and back

Claire and I visited my older son, Dave, and partner Mary Ellen in Ithaca, NY, over the weekend. Great trip with Tesla 3, supercharged all the way.

Glad we did not go farther afield:

An assortment of photos, from sailing on Canandaigua Lake, views of the north shore of Seneca Lake, looking out over Cayuga Lake from Cayuga Heights, shots at Taughannock Falls State Park near Ithaca, and Buttermilk Falls State Park, and a vid of Claire feeding chickens.

## Opposing Canadian hydropower, an opposition which supports local renewables?

Ilana Cohen of the Pulitzer prize-winning Inside Climate News reports how some environmental activists in northern New England are concerned about the progress of tapping Canadian hydropower to feed the electrical needs of New England. Opposition is also voiced by Canadian indigenous communities. (See article.) One reason given by activists is

Sierra Club’s Atlantic Chapter has raised concerns around the use of carbon-intense fossil fuels by HydroQuébec to substitute for hydropower if the Canadian company deems it necessary to meet New England and New Yorkers’ electricity demand. The group also warned that reliance on Canadian hydropower “would undercut financial incentives for developing local, distributed energy” as an alternative to fossil fuels.

That’s all well and good, Mr Sierra, but what if there’s local opposition to the “local, distributed energy” you seek for reasons similar to why hydropower has been opposed? Sure, New England needs zero Carbon energy. Fossil and nuclear generation is closing. Without rapid build-out local sources, particularly big solar farms and batteries, New England will back into the arms of natural gas generation or Canadian hydropower.

So, if northern environmentalists really want to see this happen, I recommend they contact their New England — and, in this case, eastern Massachusetts counterparts — and suggest they get with making the necessary trade-offs. These not only include solar farms in suburbs, but liberalized rules for placing solar PV on homes and on ground mounts in yards, and better solar access legislation which gives homeowners a right and priority to solar, over public or neighbor’s trees, for example, whether or not there are wetlands. And it also might support land-based wind turbines. Why not?

Otherwise the outcome will be a perfect division of environmental objectives, something which could have been orchestrated by carefully placed donations and whispers from an arch-enemy of the natural world like the Koch Brothers machine. And the result will be more natural gas burning and more pipelines.

A planned approach is the reason why I think ecomodernism is the way to go. And that’s the realm of technocrats. And, yes, I think that’s a good idea.

## “Charlie, the jogger, the killer, and the journalist” — Xi’an’s Og

I was deeply angered when I heard of this atrocity, to the degree that I had tears in my eyes. It was bad enough when Salman Rushdie had to go into hiding and adopt elusiveness as a lifestyle for the crime of publishing stories and having a fatwa drawn against him, but this attack stands as an offense against Western values, notably comic satire, and against rationality itself.

The loss of the actuality of Charlie Hebdo if not its memory is sufficient reason to mourn.

As I write atop this blog:

## From Xi’an’s Og …

The trial of the suspects of the Charlie Hebdo killings of 7 January 2015 (and of the subsequent days) has started several weeks ago, involving people accused of helping the main culprits, who died on 9 January. In the long flow of witnesses and victims, a case remains a mystery, the shooting of a random […]

Charlie, the jogger, the killer, and the journalist — Xi’an’s Og

### Update, 2020-10-18

A day of mourning, by Xi’an, including quote from Salman Rushdie.