This article is to inform you that I am featured in a pension risk article, in this week's Businessweek print magazine, coming out days before Christmas. I believe that it is a white-colored cover on this iconic magazine. As I always do, please support print journalism and the hard-working, lives of the people tirelessly perfecting their stories. If you are on vacation now, then the airport news store is always a great source for getting print media. This particular, well-received Businessweek article features an interesting discussion of the characteristics of relative pension risk associated with competitive pricing, on this emerging corporate risk transfer. As a broader extension, we see the concept I noticed, early on in Washington, about how systematically important financial institutions -often known as SIFIs- since the financial crisis also need to include among them the largest insurance companies. There is also a recent Additional notes section at the bottom of this article, which may be of your interest. Lastly, it's worth mentioning here at year-end that I am in the midst of selecting a charity for half of my book profits. That search will eventually finish, and for the six months or so since my book launch the donation contribution will be at least many hundreds of dollars!
Now for this article, take a moment to enjoy this magnificent aerial photograph I took on a business trip several days ago. Miles high, flying across a region near the Great Smoky Mountains. There is not much to see nor think about, right? No snow. No roads. No people. But a statistician always sees something. This scene captures the specific intersection of three contiguous U.S. states: Tennessee, Virginia, and North Carolina.
Even if you zoom in, there is also no way to tell in this case, where any of those state boundaries are. In some ways the idea harkens us back to a popular, and not well solved, 19th century European mathematical puzzle for map colors. What is the minimum number of colors one needs, so that he or she can color every contiguous region of a 2-dimensional map, without any two adjoining areas sharing the same color? This would be an interesting way of trying to understand how many Crayola crayons one would need to perform the task!
If this were a 1-dimensional problem, then clearly only two crayon colors would be needed. Say (B)lack and (G)rey. One could simply alternate these two colors, for every shape length. See this random sample below for 1-dimension:
B GB G BG B G
But for a 2-dimensional problem, we would certainly need more than two crayons. Though not as many as provided in one of those showy, Crayola 120 collections. Instead, we just need four colors (in the early decades scientists believed it was five colors). Four colors would allow for enough of a color-rotation (similar to what we have in the 1-dimensional case above), when always coloring all the neighboring states that circumvent it, say on a map.
For larger sized states, however, it turns out that we don't need more crayon colors. To see why, let's examine a breakdown of the 48 contiguous U.S. states, in particular. We show below a summary of the largest number of neighboring states - in a corner of that state. So in the picture above, clearly we show an example for each of those state's corner, neighboring two other states. That is, pick any of of these 3 states {TN, VA, NC}, and the other 2 states are neighboring it on the intersection pictured above.
How does this data of the 48 states above, connect back to probability theory? The concept of Bayesian math is to always assess the context behind probability measures (e.g., that was the point of the recent Data hounds released article). And this becomes increasingly difficult ideas to develop ideas to develop in the multiple variables we often think about life phenomenon. But here we are now seeing that there is no mathematical relationship exists -even though we may desire such- between the number of state borders, and the largest number of states in a corner of that state. After all most of the states above show to have the same value of 2 neighboring states.
Our probability conclusion is that we need to blend the number of states at the corner, with the size of the states, all to better understand our context. Returning now to our fun, map coloring exercise, there is no mathematical extension for higher-dimension shapes, such as something resembling a Rubik's Cube, or a barrel die that was used in various throwback games. In such cases there will always need to be at least n+1 Crayola crayons to color an n-shape object. And n could be any large size! This is something to consider when trying to data mine across multi-dimensional space, in order to isolate probability relationships among different variable values.
Additional notes
There are four of our blog articles that have received vast recognition recently, and we list some prominent and entertaining ones below. Unfortunately it's impossible to note every article or Tweet, but here is a worthy sample from illustrious news sources. If there is someone important who was neglected, kindly advise so that we can correct it next time.
Bankers not as dishonest as purported: This article garnered wide professional attention. About half of the reporters -who originally reported the Nature study- have since acknowledged our blog article as putting forth a convincing rebuttal to that underlying study. Among them are American Banker (sent to everyone in their news), New York Times' Science Doug Quenqua, Professor Emeritus Bownds, Technology news (which Nature itself cites!), government executive Sanford Rich, popular psychotherapist Noel McDermott, Lauren Foster (CFA) and celebrity financier Anthony Scaramucci.
Active management fallacy: While this important and engaging article was published nearly eight weeks ago, we only recently saw that it was noted by CFA, and the global finance publisher Wiley.
Aristocrats and monkeys: This was an interesting article on the probabilistic contribution to disparity, in what is a sequel to our larger Aristocrats in flyovers article. Seen in Bloomberg's Ritholtz.
Data hounds released: This is a recent article quashing the statistical significance implied when just showing historical data-mined odds. We take a closer look at what the modern version of the odd, Stock Trader's Almanac, described as a solid and very significant, year-end Santa Claus rally starting November 25. Instead we've only gotten a wild, and unnecessary scare ride, since November 25. Clearly there are better times and market signal measures -if one must- to buy or sell their allocation to risk. Seen in many places, including StockTwits, Abnormal Returns, The Whole Street, and professor and CEO on Seeking Alpha.
As always, we keep a general list of notices here. It can also be mentioned here, that one of my articles in Significance (related to blog articles here, and here) was within their top 10 read for 2014, and next year I am an eligible referee for peer-reviewed, academic statistics publications.
Now for this article, take a moment to enjoy this magnificent aerial photograph I took on a business trip several days ago. Miles high, flying across a region near the Great Smoky Mountains. There is not much to see nor think about, right? No snow. No roads. No people. But a statistician always sees something. This scene captures the specific intersection of three contiguous U.S. states: Tennessee, Virginia, and North Carolina.
Even if you zoom in, there is also no way to tell in this case, where any of those state boundaries are. In some ways the idea harkens us back to a popular, and not well solved, 19th century European mathematical puzzle for map colors. What is the minimum number of colors one needs, so that he or she can color every contiguous region of a 2-dimensional map, without any two adjoining areas sharing the same color? This would be an interesting way of trying to understand how many Crayola crayons one would need to perform the task!
If this were a 1-dimensional problem, then clearly only two crayon colors would be needed. Say (B)lack and (G)rey. One could simply alternate these two colors, for every shape length. See this random sample below for 1-dimension:
B GB G BG B G
But for a 2-dimensional problem, we would certainly need more than two crayons. Though not as many as provided in one of those showy, Crayola 120 collections. Instead, we just need four colors (in the early decades scientists believed it was five colors). Four colors would allow for enough of a color-rotation (similar to what we have in the 1-dimensional case above), when always coloring all the neighboring states that circumvent it, say on a map.
For larger sized states, however, it turns out that we don't need more crayon colors. To see why, let's examine a breakdown of the 48 contiguous U.S. states, in particular. We show below a summary of the largest number of neighboring states - in a corner of that state. So in the picture above, clearly we show an example for each of those state's corner, neighboring two other states. That is, pick any of of these 3 states {TN, VA, NC}, and the other 2 states are neighboring it on the intersection pictured above.
- 1 state has only 1 neighboring state, at its corner with the most state neighbors (Maine)
- 43 states have 2 neighboring states, at its corner with the most state neighbors
- 4 states have a high 3 neighboring states, at its corner with the most state neighbors (Colorado, Arizona, Utah, and New Mexico)
How does this data of the 48 states above, connect back to probability theory? The concept of Bayesian math is to always assess the context behind probability measures (e.g., that was the point of the recent Data hounds released article). And this becomes increasingly difficult ideas to develop ideas to develop in the multiple variables we often think about life phenomenon. But here we are now seeing that there is no mathematical relationship exists -even though we may desire such- between the number of state borders, and the largest number of states in a corner of that state. After all most of the states above show to have the same value of 2 neighboring states.
Our probability conclusion is that we need to blend the number of states at the corner, with the size of the states, all to better understand our context. Returning now to our fun, map coloring exercise, there is no mathematical extension for higher-dimension shapes, such as something resembling a Rubik's Cube, or a barrel die that was used in various throwback games. In such cases there will always need to be at least n+1 Crayola crayons to color an n-shape object. And n could be any large size! This is something to consider when trying to data mine across multi-dimensional space, in order to isolate probability relationships among different variable values.
Additional notes
There are four of our blog articles that have received vast recognition recently, and we list some prominent and entertaining ones below. Unfortunately it's impossible to note every article or Tweet, but here is a worthy sample from illustrious news sources. If there is someone important who was neglected, kindly advise so that we can correct it next time.
Bankers not as dishonest as purported: This article garnered wide professional attention. About half of the reporters -who originally reported the Nature study- have since acknowledged our blog article as putting forth a convincing rebuttal to that underlying study. Among them are American Banker (sent to everyone in their news), New York Times' Science Doug Quenqua, Professor Emeritus Bownds, Technology news (which Nature itself cites!), government executive Sanford Rich, popular psychotherapist Noel McDermott, Lauren Foster (CFA) and celebrity financier Anthony Scaramucci.
Active management fallacy: While this important and engaging article was published nearly eight weeks ago, we only recently saw that it was noted by CFA, and the global finance publisher Wiley.
Aristocrats and monkeys: This was an interesting article on the probabilistic contribution to disparity, in what is a sequel to our larger Aristocrats in flyovers article. Seen in Bloomberg's Ritholtz.
Data hounds released: This is a recent article quashing the statistical significance implied when just showing historical data-mined odds. We take a closer look at what the modern version of the odd, Stock Trader's Almanac, described as a solid and very significant, year-end Santa Claus rally starting November 25. Instead we've only gotten a wild, and unnecessary scare ride, since November 25. Clearly there are better times and market signal measures -if one must- to buy or sell their allocation to risk. Seen in many places, including StockTwits, Abnormal Returns, The Whole Street, and professor and CEO on Seeking Alpha.
As always, we keep a general list of notices here. It can also be mentioned here, that one of my articles in Significance (related to blog articles here, and here) was within their top 10 read for 2014, and next year I am an eligible referee for peer-reviewed, academic statistics publications.
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