Posted in statistics | Leave a comment

Book: 100% Clean, Renewable Energy and Storage for Everything

Professor Mark Z Jacobson‘s latest marvelous book, 100% Clean, Renewable Energy and Storage for Everything, summarized in a great one hour interview.

Posted in #youthvgov, an uncaring American public, Ørsted, being carbon dioxide, Benji Backer, Bloomberg New Energy Finance, BNEF, bridge to somewhere, Buckminster Fuller, clean disruption, CleanTechnica, climate activism, climate business, climate economics, climate education, climate hawk, climate mitigation, climate policy, control theory, decentralized electric power generation, distributed generation, ecomodernism, ecopragmatism, emergent organization, fossil fuel divestment, Green New Deal, grid defection, investing, investment in wind and solar energy, investments, Karl Ragabo, keep fossil fuels in ground, leaving fossil fuels in the ground, local generation, local self reliance, Mark Jacobson, Michael Osborne, National Renewable Energy Laboratory, Sankey diagram, solar democracy, solar domination, solar energy, solar power, solar revolution, stranded assets, the energy of the people, the green century, the value of financial assets, Tony Seba, wind energy, wind power, zero carbon | Leave a comment

“Rollin’ and Tumblin'” New York State Blues Fest

Posted in Larkin Poe | Leave a comment

The U.S. Constitution is a remarkable construct …

… 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.

Update 2020-11-27 00:01

Midnight rifts at the oasis.

Posted in #youthvgov, Juliana v United States, religion, science, SCOTUS, secularism, U.S. Congress, U.S. judiciary, U.S. Supreme Court, United States, United States Constitution | Leave a comment

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:

How Norfolk County preserves forest.

Choices.

Walpole Preservation Alliance

Posted in #climatestrike, #sunrise, #youthvgov, agrivoltaics, American Solar Energy Society, an ignorant American public, an uncaring American public, anti-science, being carbon dioxide, Bloomberg New Energy Finance, bollocks, bridge to nowhere, bridge to somewhere, Carbon Cycle, carbon dioxide, carbon dioxide sequestration, Carbon Tax, clean disruption, CleanTechnica, climate activism, climate change, climate disruption, climate economics, climate justice, climate mitigation, climate nightmares, climate policy, Commonwealth of Massachusetts, Cult of Carbon, decentralized electric power generation, development as anti-ecology, distributed generation, DNS, ecomodernism, ecopragmatism, electricity markets, emissions, evidence, fossil fuel divestment, global warming, Green Tea Coalition, Greta Thunberg, Hermann Scheer, Humans have a lot to answer for, indigenous peoples, Internet, investment in wind and solar energy, Juliana v United States, keep fossil fuels in ground, leaving fossil fuels in the ground, local generation, local self reliance, luckwarmers, mitigating climate disruption, On being Carbon Dioxide, Our Children's Trust, Principles of Planetary Climate, public welfare, regulatory capture, risk, solar democracy, solar domination, solar energy, solar power, solar revolution, stranded assets, the green century, the right to be and act stupid, the tragedy of our present civilization, the value of financial assets, Tony Seba, tragedy of the horizon, utility company death spiral, wind energy, wishful environmentalism, zero carbon | Tagged | Leave a comment

Dr Emily Shuckburgh, OBE : Where we are

Posted in Arctic amplification, being carbon dioxide, bridge to nowhere, children as political casualties, civilization, climate activism, climate change, climate denial, climate disruption, climate economics, climate grief, climate hawk, Climate Hope, climate mitigation, climate nightmares, climate policy, climate science, climate zombies, ClimateAdam, global blinding, global warming, global weirding, ice sheet dynamics, sea level rise | Leave a comment

How Norfolk County Massachusetts preserves forest

Of course, if solar photovoltaic arrays were proposed here instead, residents and abutters would come out to oppose them, including untruthfully claiming that photovoltaics leak Cadmium and other materials into soils.

“Cutting down trees is detrimental to the environment.”

Other wooded recreational areas available about Walpole.

Official Commonwealth of Massachusetts designated areas of core forest and habitat.

Note the Fisher Street forest and the North Street locations proposed for solar arrays are not included.

Posted in American Solar Energy Society, an ignorant American public, an uncaring American public, being carbon dioxide, bridge to nowhere, Carbon Tax, Carbon Worshipers, climate change, climate denial, climate disruption, climate nightmares, climate policy, Commonwealth of Massachusetts, Cult of Carbon, global blinding, global warming, global weirding, leaving fossil fuels in the ground, local self reliance, mitigating climate disruption, solar domination, solar energy, solar power, the right to be and act stupid, the tragedy of our present civilization, wind power, wishful environmentalism, zero carbon | 1 Comment

“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

(h/t Andrew Gottlieb, Association to Preserve Cape Cod.)

Posted in #youthvgov, bridge to somewhere, climate activism, Climate Adam, climate business, climate change, climate disruption, climate education, climate grief, climate hawk, Climate Hope, climate mitigation, climate nightmares, climate policy, climate science, ClimateAdam, Debbie Dooley, distributed generation, Eaarth, ecocapitalism, Ecology Action, ecomodernism, ecopragmatism, Emily Shuckburgh, global warming, Green Tea Coalition, Karl Ragabo, Mark Carney, Mark Jacobson, solar democracy, solar domination, solar energy, solar power, solar revolution, the green century, Tony Seba, wind energy, wind power, zero carbon | Leave a comment

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.

Posted in adaptation, bridge to nowhere, chaos, Content Delivery Networks, economic trade, economics, efficiency, Internet, Oligopolies, price of anarchy | Leave a comment

Wake Up

Posted in #youthvgov, Bloomberg New Energy Finance, bridge to somewhere, Buckminster Fuller, climate activism, climate business, climate change, climate disruption, climate economics, climate grief, climate justice, climate mitigation, climate nightmares, climate policy, climate science, coastal communities, coastal investment risks, ecocapitalism, ecological disruption, ecological services, Ecology Action, ecomodernism, ecopragmatism, ecopragmatist, fossil fuel divestment, global warming, Greta Thunberg, Humans have a lot to answer for, investment in wind and solar energy, James Hansen, John Holdren, Joseph Schumpeter, Juliana v United States, keep fossil fuels in ground, leaving fossil fuels in the ground, liberal climate deniers, solar democracy, solar domination, solar energy, solar power, solar revolution, Talk Solar, the energy of the people, the green century, Tony Seba, wind energy, wind power, zero carbon | Leave a comment

(We are) So Far From Home

Torcuato Mariano

The Saturday break from seriousness.
Posted in zero carbon | Leave a comment

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

Posted in adaptation, agriculture, agrivoltaics, agroecology, alternatives to the Green New Deal, American Solar Energy Society, argoecology, Ørsted, being carbon dioxide, Bloomberg New Energy Finance, Botany, carbon dioxide, carbon dioxide sequestration, Clausius-Clapeyron equation, clean disruption, CleanTechnica, climate business, climate change, climate disruption, climate economics, climate hawk, climate policy, Commonwealth of Massachusetts, Conservation Action Coalition, Debbie Dooley, decentralized electric power generation, decentralized energy, distributed generation, ecocapitalism, ecological services, ecomodernism, ecopragmatism, ecopragmatist, electric vehicles, electrical energy storage, electricity, emissions, energy, energy storage, energy utilities, engineering, environment, explosive methane, forests, fossil fuel divestment, fossil fuels, fracking, fragmentation of ecosystems, gas pipeline leaks, global warming, Google Earth, Green Tea Coalition, greenhouse gases, grid defection, Hermann Scheer, investment in wind and solar energy, investments, Joseph Schumpeter, Karl Ragabo, Keeling curve, keep fossil fuels in ground, leaving fossil fuels in the ground, liberal climate deniers, local generation, local self reliance, meteorology, microgrids, mitigating climate disruption, natural gas, nuclear power, NuScale, ocean acidification, ocean warming, oceans, On being Carbon Dioxide, plankton, Principles of Planetary Climate, public utility commissions, RethinkX, solar democracy, solar domination, solar energy, solar power, solar revolution, Stewart Brand, the energy of the people, the green century, Tony Seba, utility company death spiral, wind energy, wind power, zero carbon | 1 Comment

‘Biden voting counties equal 70% of America’s economy’

From Mark Muro, Eli Byerly Duke, Yang You, and Robert Maxim at the Brookings Institution:

(h/t Martin Sandbu of The Financial Times.)
Posted in Brookings Institution, capitalism, CleanTechnica, U.S. GDP | Leave a comment

Complexity vs Simplicity in Geophysics

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

GeoEnergy Math

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.

from Deacon_Information_Complexity_Depth.pdf

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.

Figure 1: Conventional tidal analysis by fitting amplitudes and phases of known tidal periods

This image has been resized to fit in the page…

View original post 1,040 more words

Posted in abstraction, American Association for the Advancement of Science, American Meteorological Association, American Statistical Association, Azimuth Project, complex systems, control theory, differential equations, dynamical systems, eigenanalysis, information theoretic statistics, mathematics, Mathematics and Climate Research Network, mechanistic models, nonlinear systems, Paul Pukite, spectra, spectral methods, spectroscopy, theoretical physics, wave equations, WHT | Leave a comment

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.

(h/t Scientific American)
Posted in American Association for the Advancement of Science, an ignorant American public, anti-intellectualism, anti-science, Ben Santer, climate denial, climate science, Climate Science Legal Defense Fund, COVID-19, denial, Desmog Blog, science, science denier, science education, secularism, Skeptical Science | 3 Comments

Rethinking Environmentalism

Stewart Brand at the Perimeter Institute. Sponsored by KPMG.

Posted in ecocapitalism, ecomodernism, ecopragmatism | Leave a comment

“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.”


― Carl Sagan, The Demon-Haunted World: Science as a Candle in the Dark

Posted in Carl Sagan | Leave a comment

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.

(*) In addition to reading and studying since May, articles about the pandemic, articles about other areas of statistics, and regarding 100% clean, renewable energy plans, as long as my unemployment compensation continued, I was aggressively looking for work. That has not worked out, and my unemployment compensation is exhausted. So I’m semi-retired now, subsisting on Social Security, a modest pension, and with the support of my wife, Claire. If something interesting comes ’round, I’ll have a serious look at it. But meanwhile, here I am.

(**) A. C. Harvey, Forecasting, structural time series models and the Kalman filter, 1989, Cambridge University Press, 4.6, "Prediction", page 223.

(***) Very recently Feroze used (such) Bayesian structural time series models to forecast COVID-19 trends for cases, deaths, and recoveries, as documented in

N. Feroze, "Forecasting the patterns of COVID-19 and causal impacts of lockdown in top ten affected countries using Bayesian structural time series models", Chaos, Solitons and Fractals (2020).

Unfortunately, Feroze does not provide the specification of the models used in the bsts R or the settings for determination of causal impact of measures taken via the CausalImpact package. Accordingly, it is difficult to comment.

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.

Posted in American Statistical Association, Andrew Harvey, anomaly detection, count data regression, COVID-19, dependent data, dlm package, Durbin and Koopman, dynamic linear models, epidemiology, filtering, forecasting, Kalman filter, LaTeX, model-free forecasting, Monte Carlo Statistical Methods, numerical algorithms, numerical linear algebra, population biology, population dynamics, prediction, R, R statistical programming language, regression, statistical learning, stochastic algorithms | Tagged | Leave a comment

Muehlenberg County

Posted in climate disruption, coal, John Prine | Leave a comment

RethinkX update on Wind, Solar, and Storage

Posted in American Solar Energy Society, Amory Lovins, being carbon dioxide, Benji Backer, Bloomberg New Energy Finance, bridge to somewhere, children as political casualties, clear air capture of carbon dioxide, climate business, climate economics, climate education, Conservation Action Coalition, decentralized electric power generation, decentralized energy, disruption, distributed generation, ecocapitalism, ecological disruption, ecomodernism, ecopragmatist, electric vehicles, electrical energy storage, electricity, electricity markets, energy storage, energy utilities, entrpreneurs, Green Tea Coalition, grid defection, investment in wind and solar energy, Joseph Schumpeter, keep fossil fuels in ground, leaving fossil fuels in the ground, local self reliance, Michael Bloomberg, microgrids, On being Carbon Dioxide, photovoltaics, RevoluSun, solar democracy, solar domination, solar energy, solar power, solar revolution, Talk Solar, the energy of the people, the green century, Tony Seba, utility company death spiral, wind energy, wind power, zero carbon | Leave a comment

“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.

Posted in Charlie Hebdo, martyrs to truth, mathematics, religion, science | Tagged , | Leave a comment

“No, COVID-19 Is not the Flu”

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

Q: What would you say to someone who insists to you that COVID-19 is “just the flu”?
A: Since December 2019, COVID-19 has killed more people in the U.S. than influenza has in the last five years.

Influenza is a significant burden on the population, but COVID-19 has had a vastly larger effect.

Read the entire interview.

Posted in coronavirus, COVID-19, epidemiology, SARS-CoV-2 | Leave a comment

dead bodies vs economic integrity

From The Financial Times.

Posted in pandemic, population biology, population dynamics, SARS-CoV-2 | Leave a comment

“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.

Posted in #sunrise, #youthvgov, Amory Lovins, being carbon dioxide, Carbon Cycle, climate activism, climate change, climate disruption, climate economics, climate mitigation, climate policy, global warming, liberal climate deniers | Leave a comment

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.

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Für alle ohne maske

h/t Professor Christian Robert.
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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.

(Emphasis added.)

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.

Posted in an ignorant American public, an uncaring American public, being carbon dioxide, Bloomberg New Energy Finance, bridge to nowhere, carbon dioxide, cliamate mitigation, climate business, climate disruption, Commonwealth of Massachusetts, Cult of Carbon, decentralized electric power generation, decentralized energy, development as anti-ecology, distributed generation, ecocapitalism, Ecology Action, ecomodernism, electrical energy storage, electricity, electricity markets, emissions, energy utilities, fossil fuel divestment, fossil fuel infrastructure, gas pipeline leaks, global warming, greenhouse gases, Hermann Scheer, indigenous peoples, leaving fossil fuels in the ground, liberal climate deniers, local generation, local self reliance, Massachusetts Clean Energy Center, mitigating climate disruption, Nathan Phillips, natural gas, regulatory capture, rights of the inhabitants of the Commonwealth, science denier, solar democracy, solar domination, solar energy, solar power, solar revolution, sustainability, sustainable landscaping, the green century, the right to be and act stupid, the tragedy of our present civilization, utility company death spiral, zero carbon | 1 Comment

Solar PV, Agriculture, and Enhancing Pollinator Habitats

 

 

Stephen Herbert, professor of agriculture at UMass Amherst, right, shows farmer Pat Canonica of Boxford how raised solar panels allow for the land underneath to remain in agriculture as vegetable gardens Aug. 31, 2017 at the UMass Crop and Animal Research and Education Center in South Deerfield.
Posted in agrivoltaics, agroecology, decentralized electric power generation, solar democracy, solar domination, solar energy, solar power, solar revolution, zero carbon | Leave a comment

“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:

I live and die as a being of reason or I have no reason for being.





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.
Posted in humor, rationality, reason, satire | Leave a comment