Archive for October, 2009
Science is fun! It is fun, because things can emerge. Things that were not anticipated. It might be that the information of the things that eventually emerged has been there before you started, but you were not aware of it.
To this day things can emerge and there is no explanation. In these cases, experiments are not done to prove or to refute something, but because of fun. I am convinced this works in most fields. And it works even today, where it might seem that in some fields everything is found out. It works with “material experiments” such as this one where Frank Rietz played with glass beads. It can be in statistics, when you “play around” with a given data-set, and probably it can happen in any discipline. To a great deal, this is why I think science is fun!
Now, sit back, and watch this, and be amazed!
update2 Thursday; October 29, 2009: the story is spreading…
update Thursday; October 29, 2009: Journal Watch Online just highlighted today a study related to the amount of plastic that birds consume
Chris Jordan took some pictures of dead albatross on Midway Atoll in the North Pacific. These pictures dramatically show to what extreme level the North Pacific is polluted: albatross-parents feed their chicks with what they think is fish, however it is garbage. The garbage can either not be digested or is poison to the chicks. In both cases they die.
I would like to point you to a fairly new webpage: The book of odds.
It’s fairly easy to guess [sic!], what this page is about:
Book of Odds is the world’s first reference on the odds of everyday life. It is a destination where people come to learn about the things that worry or excite them, to read engaging and thoughtful articles, and to participate in a community of users that share their interests and ambitions.
The founders of this page collected information for a couple of years, evaluated that data, and put the resulting statistics on their webpage. Some of them are funny, some are interesting, some are a little old. For sure, the page is interesting to check out!
It remains to remember what odds are: the odds of an event is the ratio of the event’s probability to occur to the complementary probability. An example:
The odds that a wildfire will be started by humans are 1 in 1.18 (85%). This means that about 85% of wildfires are started, intentionally or accidentally, by people
This means, 85% is the ratio of the numbers of wildfires started by humans and the number of total wildfires (in a given area over a given time, none of which is unfortunately directly mentioned in this article at the book of odds) is 100/118.
The NUPUS conference is over, the first snow of the year has fallen, a good friend is married — now I have finally some time to continue with some examples related to regression and actual weather data. I have promised that since quite a while now. Sorry!
In the first post of this mini-series on regression I looked at some basic properties of traditional regression analysis. Today I will look at two real-world examples of meteorological data and apply some of the methods of the first post. I will use some of the features introduced in Mathematica version 7 for plotting meteorological as well as spatial data. I think you can find a really great introduction at the Mathematica Blog as well as at the mathematica help-site. In the next post, I will look at some disadvantages of traditional regression analysis.
The novel features of mathematica make it fairly easy to look at the daily mean air temperatures in Munich and in Frankfurt (Figure 1). Since the two cities are located fairly close to each other, their daily mean temperatures are fairly similar. The orange dots which indicate Frankfurt are roughly at the same location in the scatter-plot as the black dots which indicate Munich.
It gets a little bit trickier, if we want to look at a different kind of scatter-plot: not at a time-series as in Figure 1 but at a scatter-plot similar to the heights of the pairs of fathers and sons (Figure 1 in the previous post, for example). Ulises at Wolfram, one of the two authors of the Weather Patterns Blog Post at the Wolfram Blog, was so kind to write a wicked little filter for that purpose, which I am sharing in the mathematica workbooks for this post (see links at the end of the post). This filter involves the Mathematica functions Intersection and Alternatives. As we have seen on Figure 1, at the same date the mean air temperature at both cities is fairly similar, three things can be expected:
- the scatterplot is expected to point upwards
- the point-cloud is expected to be narrowly confined (in contrast to the corresponding figure (Figure 1) in the case of Galton’s fathers- and sons- heights)
- the means for Munich and Frankfurt are expected to be similar
All the expectations are met, as shown on Figure 2. Additionally, the regression line and the SD line are almost identical, which is due to the fact that the correlation coefficient r is very close to 1.
As a second example, let’s compare the daily mean air temperatures in Munich and in Cape Town, South Africa (Figure 3). Since both cities are on different hemispheres, annual cycle of temperatures are phase shifted by half a year. Additionally, the range of encountered temperatures is smaller than in Munich, and always above zero in Cape Town. The corresponding scatter-plot is shown on Figure 4. Due to the phase shift, the correlation is negative and the cloud of the points of the scatter-plot is pointing towards the bottom right of the chart.
What are the differences between the two data-sets using data from Munich-Frankfurt and from Munich-Cape Town?
- if the temperature in Munich is high, then the temperature in Frankfurt is also high (and vice versa), hence there is a positive correlation in temperature in Munich and in Frankfurt: .
- if the temperature in Munich is high, then the temperature in Cape Town is low (and vice versa), hence there is a negative correlation in temperature in Munich and in Capetown:
- the correlation between Munich and Frankfurt is stronger than between Munich and Cape Town. This is also the reason, why the SD line and the regression line are more similar in the case of Munich and Frankfurt than in the second data-set.
Here are the links to the Mathematica workbooks for this post:
In the next post, I will look at some of the properties of this regression analysis.
Nobel Prize in Economics
update Thursday; October 29, 2009: here is an overview-article, “The Non-Tragedy of the Commons”. It deals like my post with Hardin’s paper, it includes additional references to Elinor Ostrom’s work, and it shows solutions how the commons can be managed well.
The Nobel Price in Economics has been awarded this year to Elinor Ostrom. Besides being the first woman who has been awarded the Nobel Price in economics, she is also the first environmental economist. The Nobel Committee explains its choice for her due to her research on “problems related to the use of commons such as fishing grounds, groundwater resources, forests and pastures”.
According to The Globe and Mail,
Dr. Ostrom’s research, and her celebrated publication, Governing the Commons, challenged the prevailing wisdom that the best way to manage something is to privatize it or regulate it.
I haven’t read any of her works, in fact I haven’t heard of hear until this morning. However, the reasoning of the Nobel committee reminded me of probably one of the top five scientific papers I have read in my university career, at a very unlikely place. I once took a course entitled “ecological engineering”, given by Allan Werker who now seems to be at a company called anoxkaldnes. In this course we spent quite some time reading and discussing the paper “The Tragedy of the Commons” by Garrett Hardin. Back then this article sparked some of the most vivid discussions I have ever had in an engineering class, including some interesting modelling exercises with BerkeleyMadonna.
Right Livelihood Award
On a related note and since it seems to be award-season, I want to point out that the right livelihood awards 2009 have been awarded to David Suzuki, René Ngongo, Alyn Ware, and Catherine Hamlin.
David Suzuki is an interesting person, has great speaking and writing skills, and has undertaken a lot of action in his life to make the world a better place. His autobiographyis a remarkable read.
Even more remarkable is a speech given by his daughter to the assembly of the UN. She’s known in YouTube as the “Girl who Silenced the UN for 5 Minutes”:
I promise to continue to post on correlation examples really soon!
the response to the regression line post was straight out phenomenal and mind-blowing. In the next sequel, we will look at some real data. I had this planned for today, but unfortunately preparing for the NUPUS conference, at which I will take part next week, takes longer than anticipated. I promise I will post on monday again.
However, I do have a suggestion for your weekend (if you’re not planning to climb up any mountains or if you are sick at home): read this!
I just found out that “the economist” has a sequel of classic debates, on various topics. The debate I’m suggesting for you to read is entitled “The value of H2O” — This house believes that water, as a scarce resource, should be priced according to its market value. Defending the motion is Mr Stephen J. Hoffmann, who recently published a book which is called just like this blog (more about this really soon). The arguments against the motion are represented by Dr Vandana Shiva.