what the birthday problem can teach us about when to have a baby

Carl Bialik at FiveThirtyEight recently posted a chart that summarizes when babies are born, which reflects attitudes and practices about scheduling inductions and C-sections. The chart shows that people are superstitious and have fewer babies on the 13th of each month, particularly on a Friday the 13th. I am not superstitious. My birthday is also on a 13th, although I was born on a Thursday. My mom had no choice in the matter because she went into labor naturally. But I’m confident she would not have shied away from the 13th.

This chart has implications for The Birthday Problem:

Given a group of n people, what is the probability that someone shares a birthday?

The canonical problem assumes that people are equally likely to be born on any day. If some days are more likely than others, then a match is even more likely. I simulated the birthday problem with a “mating season” here.

The data can be used to identify when hospitals have room shortages and when to have extra staff on hand. When I saw Bialik’s paper, I couldn’t help but think that the 13th of the month might be the ideal time to have a baby. Or the 15th. Or January 3. Or July 4.

We live in a world of limited resources, where we run some risk of not having enough of what we want. The above chart suggests that risk is not evenly distributed to all births. Having a baby on the 13th means that there is always a delivery room ready. If the hospital only has one bath for water births, you may have less competition for it. Or not. Having a baby on the 15th means that women who had babies on the 11th and 12th were discharged, leaving plenty of rooms in the maternity ward for mom and baby to recover.

When I had my third daughter, the hospital was out of rooms in the maternity ward. Only one woman was discharged, which meant that only one mother could be admitted. I was selected for the room because my daughter was born at home in a precipitous labor and accidental home birth. The staff felt that since I did not use a delivery room, I should get the room in the maternity ward. I was grateful.

This is not uncommon. You will always get a room, but you might have to wait in an uncomfortable place, such as a delivery room or elsewhere. I stayed by myself in the delivery room for hours after my second daughter was born instead of recovering in the maternity ward. It was stressful because I could not see my daughter for a long stretch of time, because security dictated that babies in the maternity ward could not leave. I was eventually taken to the maternity ward, where I discovered that my daughter was doing just fine and sleeping peacefully.

Mothers will always get a room somewhere eventually. Most women stay one to four nights in the hospital, depending on the details of the birth and their preferences about staying at the hospital if things are going fine. A hospital can be less busy for one to four days after a lull in births on the 13th of the month. I dealt with a hospital shortage after 2 of my 3 daughters’ births. None of their births were ideally timed according to my reasoning above. And none of their births were poorly timed on a busy day (see the heat map below)

So far I’ve talked about room shortage. Rooms are one type of limited resource. Staff are another. Staffing can be changed in response to trends in births, but hospital rooms cannot since there are only so many rooms in the maternity ward. Still, extra staff can make things happen to make the hospital run smoother when it’s busy. Discharges can be processed faster, for example, which can address a shortage of rooms.

I love talking about my daughters and analytics 🙂 Anyway, here is a heat map of birthdays.

A heat map of likely birth dates

For more reading:

 

 


My teaching journey: there and back again

Today I gave the keynote talk for the spring New Educator’s Workshop for teaching assistants at UW-Madison. I’m posting my slides here. My talk was entitled, “My teaching journey: there and back again.”

Abstract. I will talk about my journey from a painfully shy TA to a professor who is comfortable in the classroom and when talking to the media about research on the evening news. I will talk about strategies I used to be effective in the classroom given my strengths (and weaknesses).  Topics include time management, active learning techniques, easy ways to teach with technology, tips for managing student expectations, and things I wish I knew when I was starting to teach.

 

Blog posts that inspired my presentation:

 


Hidden Figures: my review (with a few spoilers)

“Every time we get a chance to get ahead they move the finish line. Every time.” Mary Jackson’s complaint about finding out that she needs to get a certification at an unsegregated men’s school before she can apply to engineering school summarizes the main theme of the movie. Hidden Figures follows Katherine Goble Johnson, Dorothy Vaughn, and Mary Jackson—human “computers” who worked in an all African American women’s division at the NASA Langley campus—and their trials and triumphs during the space race in the early 1960s. Intellect and ability may be color blind but opportunity was not. These capable women were used as temps, who temporarily joined teams at NASA to work on space projects based on whoever had an immediate need for a number cruncher. The opportunity to do anything beyond that (and get paid accordingly for it) was not available. The movie is based on the book by Margot Lee Shetterly and adapted by Ted Melfi (the director) and Allison Schroeder.

First of all, I really enjoyed this movie. It’s fun and memorable–parts of this movie will stick with me for a long time. I credit Octavia Spencer in particular for bringing her infectious humorous warmth to the film as Dorothy and to Ted Melfi for ensuring the movie felt authentic, both historically and on a personal level. The main characters do not feel like cardboard cutouts of real people. There is even discussion of math in the film. Melfi studied the math in depth before writing key scenes to make sure he could explain it to a lay audience. His hard work pays off. A high point of the movie involves a discussion of elliptical orbits and Euler’s method. The historically accurate details in the film brought authenticity to the movie. I knew some things were true before fact checking later. An IBM mainframe is delivered and cannot fit through the door. John Glenn tells NASA managers to “get the girl to run the numbers” before a final check before his historic Mercury 7 flight. The “girl” is Katherine Goble Johnson who saves the day with math.

The movie also succeeds because it makes the obstacles the women faced feel real and difficult to overcome. There were many obstacles to their success. This was the era of segregation, which meant separate bathrooms, drinking fountains, coffee pots, and sections in the library. There was only one women’s “colored” bathroom on the enormous NASA Langley campus. The human computers were being replaced with an IBM mainframe. Checking out a book on FORTRAN to program the mainframe at the public library was an ordeal because FORTRAN books were not in the colored section of the library.

While the movie follows a familiar formula, it feels fresh. Through Melfi’s steady direction, Hidden Figures clearly conveys that the seemingly small issue of the African American women not having a nearby bathroom is in fact a huge obstacle. Several scenes follow Katherine scurrying to and from the bathroom across the NASA campus (half a mile each way) for bathroom breaks in a skirt and high heels, the required dress code at the time. Each time, the plot movies forward in key ways. Katherine makes important contributions to the project, yet her name cannot go on the report since computers cannot author reports. Engineers can only author reports, so a white male engineer gets credit for Katherine’s work and Katherine is for the moment written out of history. Again, Melfi’s direction communicates these ideas visually. Throughout the movie, we understand that the myriad of small institutional barriers to inclusion and equal opportunity were like a ton of feathers that impeded all but the brightest stars from achieving what what anyone should be entitled to have. We still have institutional barriers today. Melfi doesn’t tell this to the audience, but instead lets them connect the dots on their own.

Most of the movie follows Katherine, Mary, and Dorothy at work, but they each have key scenes outside of work with their families. Early in the movie, we only know the main characters as African American mathematicians. Only later we learn that they have families. Katherine goes home and we discover that she is a widow and single mom to three daughters. This scene was my favorite. Katherine returns to her daughters after a long day of work. Her three daughters are fighting as they go to bed and irritated that their mother has to work. She does not apologize for working, and instead calmly gets her daughters to stop fighting and puts them to bed. She is both a good mother and mathematician. The director Ted Melfi got this right. Katherine eventually remarries in the film. From the moment she meets her future husband (Jim Johnson), he understands that she and her children are a package deal and the children are at the center of their relationship. All three women are working mothers pass on their values on to their children in a world where the rules are not fair. Dorothy and Mary tell their young children about injustices. Mary and her husband do not have the same temperament, but her husband supports her working toward an engineering degree. Later Mary becomes the first black women engineer to work at NASA.

This movie is not completely original but it was nearly perfectly executed. This movie will stick with me for a long time, and I’m anxious to see it again, this time with my daughters. I highly recommend it.

What did you think of Hidden Figures?

For more reading and listening:

 

 


chocolate chip cookies are Poisson distributed

I asked for examples of things that are Poisson distributed in class. One student said the number of chocolate chips in a cookie are Poisson distributed. He’s right.

Here is the intuition of when you have a Poisson distribution. First, you should have a counting process where you are interested in the total number of events that occur by time t or in space s.  If each of these events is independent of the others, then the result is a Poisson distribution.

Let’s consider the Poisson process properties of a chocolate chip cookie. Let N(t) denote the number of chocolate chips in a cookie of size t. N(t) is a Poisson process with rate y if all four of the following events are true:

1) The cookie has stationary increments, where the number of chocolate chips in a cookie is proportional to the size of the cookie. In other words, a cookie with twice as much dough should have twice as many chocolate chips (N(t) ~ Poisson (y*t)). That is a reasonable assumption.

2) The cookies has independent increments. The number of chocolate chips in a cookie does not affect the number of chocolate chip cookies in the next cookie.

3) A cookie without any dough cannot have any chocolate chips (N(0)=0)).

4) The probability of finding two or more chocolate chips in a cookie of size h is o(h). In other words, you will find at most one chocolate chip in a tiny amount of dough.

All of these assumptions appear to be true, at least in a probabilistic sense. Technically there may be some dependence between chips if we note that bags of chocolate chips have a finite population (whatever is in the bag). There is some dependence between the number of chocolate chips in one cookie to the next if we note that how many chips we have used thus far gives us additional knowledge about how many chips are left. This would violate the independent increments assumption. However, the independence assumption is approximately true since the frequency of chocolate chips in the cookie you are eating is roughly independent of the frequency of chocolate chips in the cookies you have already eaten. As a result, I expect the Poisson is be an excellent approximation.

Picture courtesy of Betty Crocker

 


Punk Rock Operations Research T-shirt

I enjoyed designing and wearing a Punk Rock Operations Research T-shirt at the INFORMS Annual Meeting. I brought a few extras and sold out at the conference. If you want to purchase a T-shirt, you can order one here at CafePress.

 

Ed Kaplan, INFORMS Member-In-Chief

I am honored that Ed Kaplan, INFORMS Member-In-Chief, wore my T-shirt!

 

Matt Saltzman purchased a T-shirt but wasn't wearing it yet in this picture.

Matt Saltzman purchased a T-shirt but wasn’t wearing it yet in this picture.


10 things you can do with an industrial engineering degree

Kim Christopher (BE IE, MBA) won my department’s Distinguished Achievement Award for alumni. She visited my department and gave a seminar about her career. She had worked in many roles in many industries and talked about her experience.

Kim’s list of what you can do with an ISYE degree:

  1. You could manufacture products.
    • Kim interned at General Motor, Procter & Gamble, and the military (she made motors for the F14 fighter jets)
  2. You could research new technologies.
    • Robotics, expert systems, intelligent transportation systems.
  3. You could sell products or services.
  4. You could market or communicate technical things.
    • Engineers companies need help telling their stories.
  5. You could develop new products.
  6. You could improve quality.
  7. You could run a business.
  8. You could teach.
  9. You could have a dual-career family.
    • I loved Kim’s enthusiasm for wanting it all, having it all, and not apologizing for it.
  10. You can give back.

Other takeaways:

  • Some of Kim’s achievements were due to being opportunistic when good opportunities came by. She was able to implement an intelligent bus transportation for public transit in Napa Valley because only public leaders there were receptive.
  • Sales was more fun than engineering.
  • Kim worked on an MBA while working full-time. It was grueling and expensive, and she has no regrets.
  • Kim said her choice of a husband was her most important choice along the way.

Kim Christopher

Kim Christopher


analytics for governance and justice

In May 2016, the Office of the President released a report entitled “Big Data: A Report on Algorithmic Systems, Opportunity, and Civil Rights” that challenges the idea that data and algorithms are objective and fair. The report outlines President Obama’s plan for identifying and remedying discrimination in data and automated decisions by making data and processes more open and transparent.

This is part of the White House’s plan for data driven governance. With better data, you can make better decisions. I love it.

President Obama said that “information maintained by the Federal Government is a national asset.” He started data.gov, which is a gateway to government agency data to researchers and the public.

Created as part of the President’s commitment to democratizing information, Data.gov makes economic, healthcare, environmental, and other government information available on a single website, allowing the public to access raw data and use it in innovative ways.

Data.gov began as a tool to reduce government waste, but it has since branched out to meet other goals, such as the aforementioned social justice issue inequities. The White House created the position “Chief Data Scientist” and hired DJ Patil to fill the position.  He has been working on breakthroughs for cancer treatment lately.  The White House hosted an “Open Data Innovation Summit” in September 2016 to share best practices regarding the opening up of government data. While I applaud the trend of open data, it is necessary but not sufficient for reducing inequities, informing decisions, and cutting government waste.

I am less familiar with the big wins that data driven governance has had. Please let me know what they are in the comments. I have no doubt that there are big wins. With better data, we can make better informed decisions.

Data is a huge topic, and there is a lot of data out there. The government investing in archiving and analyzing data is necessary for breakthroughs to happen. There are a lot of people involved in this effort. My colleague, Dr. Patti Brennan now heads the National Library of Medicine. The National Library of Medicine is composed of data to support medical research, and I’m glad we have a Wisconsin ISYE Professor Emeritus and rockstar in charge.

I started this post before the election. I hope the project continues its momentum in the next administration to have an impact. Only time will tell.

 

 

Data topics at data.gov

Data topics at data.gov