A Drifting Bias?

Here is an interesting dataset that I have come across after grad. school.  The picture below illustrates different measurement standards for heat.  For those of you not familiar with measurement standards (or standards for short), these are items that scientists/metrologists claim they know the value, of some attribute of interest (such as heat, mass,etc.), very well (or to within a certain amount of error).  The researchers use these standards to "check" their measurement devices (we will call them gauge for short), i.e., is the device making accurate and precise measurements.


In a perfect world, a gauge should make measurements that are exact, meaning the measurement is exactly the value of the item's heat, for example.  Unfortunately, we live in a not-so-perfect world and the measurements we receive are not exactly the true value of the heat.  This error could come from changes in the rooms environment where the measurement was made, different operators, the gauge makes measurements that are too high, etc.    It is the job of a statistician to somehow quantify all these sources of error and assess the gauge or the item being measured.

Anyway, back to the data set.  The picture below is an example of heat standards being measured on a gauge (calorimeters if you are curious). The different shades of gray correspond to different heat standards (in watts).  The y-axis is the measured value on the gauge divided by the claimed true value of the item (the ratio helps since these are assumed to be multiplicative error models, i.e., the error increases with the increasing heat standard) and the x-axis is time (in days).  On the y-axis, I then subtracted one from all the values to help illustrate the bias more.

The blue line is a smoothing spline to show the trend in the data with associated confidence intervals (I think pointwise) about this line (gray ribbon).  If this gauge was unbiased (meaning it doesn't make measurements too high or too low), the points would be centered around zero (or one if I had the raw data).  This is not what we see, however.  Instead, the bias seems to drift with time.  If things were simple, we would expect to see a constant bias with time, e.g., all the values are centered about .001.

Now I know what you are thinking, on average it looks like there is not a bias, and this may be true, but this doesn't help when we are interested in the bias at a specified point in time; we would like to be able to account for that bias.

The researchers were excited to see this plot because their experience told them that there must be some sort of bias that is changing with time.  They just hadn't gotten around to creating a plot like this. For those of you still curious why there is a drifting bias, the scientist think that there is a heat source correlation present.  What I mean is that these units are put into a water bath.  When they remove the item and put in a new one, there may still be some sort of residual heat or something left from the old item.  Since these items are of different heat amounts, this residual heat could be large or small.  Either way, the researchers think this residual heat is still present and affecting the current measurement.

Unfortunately I have not had the time to solve this problem, though I hope to one day and even have an interested colleague to collaborate with.  I would love to hear your ideas.

 

 LA-UR 11-02586

Update:  Professor Ivan Ramler recently was given some funding for us to work on this!  Stay tuned for what we discover.

Advice I Received from an Experienced Mathematician

Not too long ago (I would say a month and a half) I attended a lecture by a mathematician named Mac Hyman on how to have a successful carrer in Science (I have two links for him, one is for his Tulane Univ site and the other is his Los Alamos site).   This was truly one of the best talks I ever attended.  The abstract to the talk is the italicized text at the end of this post.  Before I describe the talk let me first mention that this talk was directed at students.

His introductory argument was that those who have or had the best careers are not always those who were the top students in Grad school (always the best in the class and won dozens of awards), like we would expect.  Surprisingly (at least to me), it is commonly those who were mediocre in school.   This doesn't mean that if you were a top student in grad school that you are not going to have a great career, it just doesn't guarantee that you will (and likewise if we were mediocre we are not guaranteed a great career).  This was very encouraging to me since I definitely was not the best student (I tended to be lazy haha).

In his opinion, based off of a lifetime of experiences and observations, there were three keys to developing a great career.  These are:

1. Work on what you are passionate about
2. Exploit your natural talents and develop your professional toolbox
3. Finding the right work environment that will support you in your career

I will paraphrase what I remember about these different bits of advice.

1).  This is very important.  If we are going to do truly great work, it needs to be on something we are passionate about.  This may seem like an obvious tip, but I think we would be surprised at how many of us do not work on what we truly love.  If we are truly passionate about something then we enjoy going to work, which I think speaks for itself.  Additionally, if we are working on something we are passionate about, then we will get that strong feeling of satisfaction in what we do, which will give us a more rewarding life.  Keep in mind though, this passion does not have to be static.  One day we may find something fascinating, but the next day, that spark is gone.  The key is we always need to be pursuing what we are truly passionate about.

2).  Prof. Hyman talked about how all humans have talents.  He emphasized that we need to exploit these talents in our work.  For example, Jay Leno is a natural for presentation and comedy, it only seems obvious that he pursued a career that exploits these talents.  He also talked about how all humans also have weaknesses or abilities that we do not do naturally.  In our careers these can become anchors, something that holds us back.  It is then up to us find a crutch that we can lean on.  His best advice for finding a crutch is a colleague who has a natural talent for our weakness.  He claims that his best work in his career came when he did work with a colleague who was a natural at his own weakness and vice versa he was a crutch for his colleague's weakness.  An example he gave was Microsoft.  Apparently Bill Gates had a natural talent for computers and his weakness was business.  On the other hand,  Paul Alan was a wiz at business and combined they became an extremely powerful and successful business.

3).  This was Prof Hyman's final bit of advice.  Tips 1) and 2) alone are not enough, we also need to find an environment where we will not only be allowed to pursue our passions, but be inspired and encouraged as well.  From his presentation "We want to strive to work in a culture of discipline with a rigorous, but not ruthless, culture where people share your work ethics and desires."  Additionally "Seek out clock builders, not time tellers who never stop trying to become qualified for the job."

Finally I will end this passage with some good quotes from the talk.  I hope that many of you find this somewhat helpful as it did for me.

• "If you could do anything for the next ten years, what would it be?"
• "Passion isn't dictated, it's discovered"
• "Give yourself permission to follow your heart"
• "It would be crazy not to follow your heart and spend part of every day engaged in something you are passionate about."
• If you don’t think that have enough talent to create a great strength, then you haven’t found your talent.
• "Working with the right people will be your most important asset. Count on missed opportunities if you work around the wrong people"
• "A genius at building sundials will not receive recognition by working in the shade."
• "Why strive for a great career? 
  If you are engaged in work you love and care about, for 
  whatever reason, the question needs no answer. The question is not why, but how."

The choices that scientists make early in their careers will impact them for a lifetime. I will use the experiences of scientists who have had great careers to identify universal distinguishing traits of good career choices that can guild decisions in education, choice of profession, and job opportunities to increase your chances of having a great career with long-term sustained accomplishments. 

I ran a student internship program in Los Alamos National for over 20 years. For the last couple of years I have been tracking the careers past students and realized that the scientists with great careers weren't necessarily the top students, and that some of the most brilliant students now had some of the most oh-hum careers. 

I will describe how the choices made by the scientists with great careers were based on following their passion, building their talents into a strength supporting their profession, and how they identified a supportive engaging work environment. I will describe some simple guidelines that can help guide your choices, in school and in picking the right job that can lead to a rewarding career and more meaningful life. 

The topic is important because, so far as I can tell, life is not a trial run - we have one shot to get it right.  The choices you are making right now to planning your career will impact your for a lifetime. 

Please join us for an engaging discussion on how to make the choices that will lead to a great career

Fear Not

Do not be troubled.  I am currently working on two posts, I just have not had the time to complete them.  Stay tuned as they should be up soon.  Thanks for your patients.

A Freaking Cold Star (Warning Science Content)

NASA announced a new discovery recently.  Apparently they have a satellite that is built for detecting longer wavelength radiation known as WISE (Wide-field Infrared Survey Explorer).  I believe it mainly detects infrared radiation but am unsure if it can detect longer or shorter wavelengths.  This satellite is able to detect star-like bodies known as brown dwarfs (potential stars that did not have enough mass for fusion to happen, essentially like Jupiter).  The brown dwarfs themselves have been known for a while and the surface temperatures of these tend to be > 700 degrees Fahrenheit.   Astronomers using WISE have detected brown dwarfs with surface temperatures as low as 80 degrees Fahrenheit (we could swim in hydrogen haha)!

That is why I love astronomy, there is just SOOOO much to discover.  Read more about it at:

http://www.nasa.gov/mission_pages/WISE/news/wise20110823.html

What is Statistics (Warning Science Content)

There is one question that has been plaguing me since I began to take my first statistics course as an undergrad at UNM.  That question is "What is Statistics?"  I could of course plug away at google and wikipedia and give some encyclopedia definition as an answer.  For example, from wikipedia, statistics is:


the study of the collection, organization, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments.

This approach is sufficient for answers to many other questions.  For the answer to my question in particular, however, yields a lackluster answer.  Philosophically, I do not like this definition.  I don't think that this definition is necessarily wrong (though I question what is meant by organization), I just think it removes the sexiness that our founders worked so hard to achieve.   

John Tukey is sexy!

If some Ferarri driving mustached man wearing a hawaiian shirt and too short shorts held a magnum to my face and asked "What is statistics?" Could I answer him?  Would my answer satisfy his internal philosopher?  Could I keep my eyes off his thighs?  Alas I cannot say.  But, if I had to come up with an answer I would say:

Statistics is the science of uncertainty.

and full of hunks!

To help explain what I mean by the science of uncertainty, consider the very simple equation from physics:

or as we know it, Force = mass x acceleration.  This equation is what we call "deterministic".  What deterministic means is if we know the acceleration and the mass perfectly, then we can predict the force perfectly.  The following figure illustrates what I mean, here I will let acceleration come from gravity and assume it is 9.8 m/s^2.

Notice that in this plot, with a fixed value of a and for various values of m, we see the force plots as a straight line (with slope = a and intercept = 0).  So if you give me any mass, I can tell you exactly the force being applied to it just by using this line.

Unfortunately life is never that perfect.  When we measure things, being human, we measure them with error.  So in reality the above plot would look something like the plot below:

Notice that now, the point are no longer on the straight line but deviate from it slightly.  The black line on the plot is the same line from the first force plot.  Here is where the statistician comes, our job is to not only model the true physical equation (the force equation) but to also mathematically model how the points deviate from the plot (we add noise to the signal).  Our force equation may now change to:

where the last "e" term represents the random noise we added to the signal.  The next plot shows this mathematical model (blue line) "fit" to the points where the gray line represents the error in how well our line is fitting the points:

Of course this example overly simplifies what we do.  Typically the data we see does not have a known physical relationship (so we look for one), the data we get tends to be really noisy (points are further away from the line in the 2nd plot), and we tend to have many more variables. 

I hope this post begins to illustrate what it is we do and I also hope this shows that we are more than just number crunchers and accountants (yes I have been equated with an accountant).

My First Post (HAHA Cliche title)

Why write a blog...I have no freaking idea.  For whatever reason, I just feel like writing.  I am realistic; I do not expect thousands of people to view these entries.  I will be happy if >1 persons follows this.

What should one expect?

Great question.  At the current version of this post I am planning on writing about my struggles and victories in the world of Statistics.  In addition, I plan on writing about my travels (either domestic or foreign).  I want to remember all the places I have visited so I figure a blog would be a good "diary" if you will.  This was motivated by my good friend Dan Cancilla and his blog about living in Japan for a year (thanks Dan C if you ever read this).

My most recent trip was to an odd conference in Palm Dessert ,CA.  This was a short trip but I hope to get a blog entry about it while it is still relatively fresh in my mind.   Also, I will be heading to the majestic city of Kansas City, MO in October for the Fall Technical Conference so stay tuned.

One last note: I am calling myself Dr Brian because this is probably the only place I will ever see "Dr" in front of my name.  I work at a place where you could literally through ten cats and a Jawa in the air and 5 of the cats will hit someone with a PhD, so I am not that special haha (the Jawa on the other hand is another Bernoulli trial).

Enjoy and thanks for reading.