I often use bootstrapping when I need to get an estimate of some parameter, but that is because I have access to sufficient computational resources to to just do run my analysis as much as I want. But that has not always been the case and the usual method before boot strap was jackknife. The jackknife approach is a simple leave-one-out approach, so that given n observations, then for i = 1, 2, \ldots, n, calculate the statistics with the ith element omitted.

There are some natural advantages to this. The most important of them is that it is relatively easy to code. An implementation in R would be only 5-6 lines of code. Another advantage is that it is easy to show the outcome’s validity. For instance, if used to calculate the mean of a dataset, it is trivial to prove that the result is the same as the mean calculated the straightforward way. Other statistics, while not necessarily resulting in the same answer, can be shown to be valid estimators, as well.

There is a downside to this, of course. For larger datasets, it can be time prohibitive to use jackknife. After all, it must find n estimates forn observations. If n = 1000, this is not a big deal. But if n is in the hundreds of thousands and the statistic being calculated in relatively intense, like ordinary least squares, that is a lot of computing to do. But even then, this is not all bad. The task is embarrassingly parallel since individual calculations of the statistic are uncoupled with each other.

But I am lazy, and I will probably stick to bootstrap.

One of the most well-known aspects of Confucian thought is the importance of the social order. Confucius thought it was important that everyone know their place in society. This idea is summarized by Confucius:

Let a prince be a prince, and ministers be ministers; let fathers be fathers, and sons be sons.

Analects XII

But it means so much more. This is an extension of the filial piety idea, and shows that everyone’s place is both defined and ordered. That is, sons are beholden to fathers, wives to husbands, but also subjects to their king. This matters because if adopted as widespread though, leads to extreme social stability. This is one of the reasons by China has been remarkably stable for more than 2500 years.

Of course, the reason we study history is to help us understand the future. Right now, the world is event that can potentially upend the social order, globally. COVID-19 has exposed gaping holes in political, economic, and social systems, globally. That’s interesting, but what’s more important is how people respond to those holes. Extreme social stability, such as that proposed by Confucius may mean little changes in societies influences by Confucian thought. On the other hand, nations like the United States and France ground their founding myths on the importance of revolutionary change. What changes and what does not will tell us a lot about how people think.

The founding myth of China revolves around the Three Sovereigns and Five Emperors. Unlike later formal dynasties, even if prehistoric like the Xia Dynasty or Shang Dynasty. This period, before the Xia Dynasty, came in the late Neolithic period and probably ended between 2100 and 2050 BCE. While prehistoric, we know of it from later oracle bone inscriptions. The Three Sovereigns and Five Emperors were likely mythical, but that does not matter much because the they provided key examples of how to govern that would lay the foundation of Chinese of political thought to this day.

The distinction between the Three Sovereigns and Five Emperors is important because the Three Sovereigns were regarded as god-kings, those from another plane who came to Earth. They came and used special powers to heal the sick and tend to individual lives. In addition, they introduced the Chinese people to what we might call staples of civilization such as agriculture and writing, though no written records survive. Their time in China led to a period of great peace and prosperity as people adapted to their new ways of life and benefited from economic and societal changes.

The Five Emperors, on the other hand, were ordinary men, but are traditionally regarded as providing similar contributions. One, Huangdi (the Yellow Emperor), is said to have given the Chinese people medicine and mathematics. Another, Zhuanxu, dammed numerous streams, and Shun was the hero of a great flood. Together, we see an early civilization going through trials and tribulations, and giving credit to leaders for surviving those trials. How much of this was the result of the Emperor or the Emperor receiving credit for the work of the society is not clear.

The entire period of the Three Sovereigns and Five Emperors is viewed as a gilded age in Chinese history, as the times of founding myths often are. The Five Emperors would later be held up as embodying the important features of leadership of different philosophical schools, during the Hundred Schools of Thought period. In particular, they would dominate the thinking of later Confucianists who saw, in particular Emperor Yao, as ruling with supreme benevolence and grace.

Everyone is talking about social distancing, but nobody seems to understand why it works. This is what I wrote for someone on Facebook.

So with any disease, there’s a bunch of metrics associated with how fast and far a disease will spread. Kind of the freshman epidemiology one is called R_0, pronounced R-naught. It is the expected value of the number of people an infected individual will pass the infection on to. Things like social distancing, closing schools, etc., have the effect of pushing down R_0. There’s a lot estimates out for the COVID-19 R_0, ranging from just over two to just about 2.5. My own models for Hebei just gave up and went home crying.

Now, for comparison, during a normalish year, the R_0 of influenza is right about 1.5. Ebola is just about 2. Measles is estimated between 12-18. MERS, from a few years back, was less than 1. Less than 1 means the infection will die out on its own. Anything greater than 1 means it will just keep going until it runs out of people, similar to Larry King with wives. This is the secret to understanding the “flatten the curve” plot.

Using the picture above, I have labeled 2 points, t_{\alpha} and t_{\beta}, as the two points where the unmitigated curve crosses the dashed line. The dashed line can actually be any value, it is just the hospital carrying capacity in this plot. If that represents n_\star people who are infected, then we can expect in the unmitigated case, those n^\star people to get n^\star \times R_0 people infected in the next time step, t_{\alpha+1}. At t_{\alpha+2}, it is n^\star \times R_0 \times R_0, and this is how exponential growth works. At the peak of the curve, it starts running out of people and the epidemic begins starving. Note, that only half the infected people over time are infected at this point. Life is still going to suck.

In the flattened curve, as I said, the effective R_0 is reduced. Let’s call it R_0^\prime, but for this discussion, also assume it is still above 1. The flattened curve touches the dashed line at t_{\beta}. This is still n^\star people infected. After this point, at t_{\beta+1}, we can expect n^\star \times R_0^\prime people to be infected. And at t_{\beta+2}, we can expect n^\star \times R_0^{{\prime}2} to be infected.

This is where we get into hopes and dreams. This chart is aspirational. The objective is to push the peak of the curve, where the epidemic starts to starve, under the dashed line. This is about keeping the hospitals from overflowing. If this curve we actually drawn to scale, the area under the left half of each curve, representing total infections, would be the same. But there’s also a practical aspect that the lower R_0 is, the lower the peak is anyway and fewer people get sick, since we actually do not have perfect mixing within the population, which would allow everyone an equal chance of contact with an infected individual.

But we have to remember, R_0^\prime is only an effective value. As soon as we all start playing in the sandbox again, it goes back up to its true value. There are more permanent mechanisms for driving down R_0, and those are vaccines. This chart is about protecting hospitals. The real goal should be to push the starvation point out passed the point where some magic threshold number of individuals are immune, due to either recovery or vaccination. That is probably between 70 and 85 percent of all people, assuming 100 percent immunity from prior contact or vaccination.

In practice, these curves both are jagged and have longer tails. The model is a tool for understanding reality, not reality itself. But it provides quite a bit of insight into how social distancing can work. But you can probably skip the face mask.

Below is the synopsis of the proposed recommendations from the Charter Review Commission. Please come by our hearing tomorrow night to discuss these with us.

I am very happy to announce that the Handbook for Military and Defense Operations Research, coedited with Natalie Scala, has been published by CRC Press. The electronic copy is available now and the print copy will be on Amazon on March 2! It was a lot of fun to work with Natalie on this, and we jointly chaired several sessions at last fall’s INFORMS conference in Seattle dedicated to the topics covered here.

From the back of the book:

Operations research (OR) is a core discipline in military and defense management. Coming to the forefront initially during World War II, OR provided critical contributions to logistics, supply chains, and strategic simulation, while enabling superior decision-making for Allied forces. OR has grown to include analytics and many applications, including artificial intelligence, cybersecurity, and big data, and is the cornerstone of management science in manufacturing, marketing, telecommunications, and many other fields.

The Handbook of Military and Defense Operations Research presents the voices leading OR and analytics to new heights in security through research, practical applications, case studies, and lessons learned in the field.

Monte Carlo is a beautiful process that can be used to address many, many problems. One of my favorites is that it can be used to estimate the value of \pi. First of all, we know that \pi is the ratio between the radius of a circle, squared, and its area. We can use that to Monte Carlo to estimate this ratio.

If you are not familiar with the Open Science Grid (OSG), it is a large high-throughput computer available as a national user facility. Unlike some other supercomputer facilities, the OSG is not intended for tightly-coupled jobs. And calculating \pi via Monte Carlo is a very loosely-coupled job. In fact, one of the samples for using the OSG in R is exactly this.

About a year ago, I redid the sample using the newish programming language Rust. Rust is getting a lot of press as a new systems programming language and a lot of its memory safety features. I think this makes it a good candidate for numerical programming. So I ported the R example over to Rust, which required a bit of work, but was doable. You can see the result here:

Using Rust on the Open Science Grid

I will admit that the Rust programming language fascinates me. It’s got all the things I want in a programming language, that I normally get from C, and also gives me some measure of protection against really screwing up. Not that I do that much…or even have a use for, anymore.

Of course, there’s nothing quite like a physical analog, and this physicist decided to use a shotgun to replicate the Monte Carlo approach!

Do not try this at home.

The Howard County Charter Review Commission has spent about a year now reviewing the County Charter. We’ve held a number of public hearings. And we are currently drafting a set of preliminary recommendations. The report is not ready yet, and will probably be available before the end of February.

On March 3, 2020, the Charter Review Commission will be holding a public hearing on the draft recommendations for review before they are presented to the County Council later this spring. The hearing will be at 7:00pm in the Banneker Room at 3430 Court House Drive, Ellicott City.

I will post a copy of the draft report as soon as it is available.

Find out more about the Commission and its work at the official website:

No matter what we consider the internal representation, the data will be stored linearly in memory. If we are using a programming language like C, we would use something like this to define a two-dimensional array for a 2×2 matrix:

float matrix[2][2];

Now, there’s a lot of different ways to represent this, so let’s say this is without loss of generality. This would give us four consecutive memory locations. Even if we think of it as a 2D array, some sort of call like matrix[2] is equivalent to matrix[1][0]. Same in any C-like language, such as C++ or Java.

I have no idea how it works in Fortran. But for a lot of interpreted languages, R, Python, MATLAB, etc, memory organization is kind of irrelevant. We are not going to access memory directly like we would in C. I just hope those languages can keep better track of the structures than I can.

Moments ago, I received an email from the Elizabeth Warren campaign:

We are thrilled to inform you that your name was submitted to the Maryland Democratic Party on our approved list of candidates.

I am pleased to announce that I am on the ballot in April as a representative to the Democratic National Convention as a pledged delegate for Warren.

Two years ago, I said one day Trump will no longer be president and we cannot build an entire party around being anti-Trump. We must also have policies that make America better. I stand by that today. We have to build a Democratic Party capable of leading the nation. That is why I am running for delegate.