Archive for October, 2010

Why is the history of stereology so muddled?

October 13, 2010

I am often surprised at how people get the history of stereology wrong. Is it really that hard to get it right?

Recently an old article has been passed around the internet like some hoax letter. It makes many of the old mistakes. It tries to give Cavalieri’s work a modern twist by assigning work to him that isn’t done for at least a century. It gets the date of Buffon’s work wrong by 44 years. It assigns the date to the end of his life instead of the early years. Even Delesse is given credit for something he never did.

A while back I was looking into an issue with point counting. I never really knew where it came from although there are reports it was invented by a geologist and then reinvented independently by another geologist. Turns out that biologists invented point counting, not geologists. In fact, it was the rage for many years before the geologists learned about it.

What’s interesting is that many articles and books get it right. Many get it wrong.  The dividing line is 1979. Anyone want to venture which famous book on stereology got it wrong first? Here’s a little juicy tidbit. The geologist erroneously given the honor of inventing point counting in 1930 gave an address in 1938 in which he laments not making use of the the new and efficient method of point counting.

It is also fair to ask if all of this matters? Well it does. People place references in articles to justify their methods. Many articles use references to articles that do not use the stereological methods they employ. Does that sound like one of those health hoax letters that list all sorts of articles as references only to find out that the articles are not about the subject matter? That’s what it looks like, doesn’t it?

The history of stereology was muddled in 1979. The errors are not being corrected, but rather they are being increased by the recent rehash of an old article that is flawed in many, many ways.

Are designed based stereological methods unbiased?

October 12, 2010

There is a common misunderstanding that design based methods are by definition unbiased. That is simply not true. There are those that have said to me, “It’s design based because I designed this idea. It is designed and therefore unbiased.” I think that latter comment tells you that being a designed based method is not necessarily unbiased. I realize that the person making the comment was unclear about the meaning of design based, but that’s the way it happened.

In a design based approach it is is possible to show whether or not a method is unbiased. It doesn’t mean that biased can’t creep in if the method cannot be implemented properly, but at least there is the hope that the biases introduced during the implementation of the method are not overwhelming.

You might ask yourself if bias if really all that bad. Does it really matter if a method used in stereology has bias? What is that doing to the result? If the amount of bias is small relative to the value being determined, then it might not be bad if the method is biased.

Suppose a method had a bias estimated to be less than 5% and the data showed a 20% difference between control and experimental, then the 5% is not important. The method would be a reasonable method if it saved work.

Unfortunately, biases are difficult to determine. Showing that the bias is less than a certain magnitude is usually impossible.

That is why design based methods that are unbiased are favored. If the method can be shown to have zero bias, then the issue is how close to the mathematical ideal is the implementation.

Typical errors in online stereology information

October 10, 2010

Recently an old article of sorts has been spread around the internet. This article makes a number of claims that are not grounded in truth.

Consider the following:

In 1637, Bonaventura Cavalieri, a student of Galileo Galilei in Florence during the high Italian Renaissance, showed that the mean volume of a population of non-classically shaped objects could be estimated accurately from the sum of areas on the cut surfaces of the objects (right). The Cavalieri Principle provides the basis for the volume estimation of biological structures from their areas on tissue sections.

It’s true that Cavalieri did publish something in 1637 and he was associated with Galileo. Most of the rest is quite wrong. For instance Cavalieri was not a student. He was a professor at the same university as Galileo. Galileo and Cavalieri had somewhat of an academic problem since Galileo had his own ideas on the subject called infinitesimals. Cavalieri’s ideas did not agree with Galileo.

The real problem here is the math. The statement here about the work of Cavalieri is completely wrong. What Cavalieri’s theorem does is to compare the volumes or areas of two objects of equal height. Let’s consider only volumes here. Two objects are the same height if two parallel planes touch the tops and bottoms of both objects. Cavalieri goes on to prove that if any parallel plane in between the top and bottom planes intersects the two objects and the areas on the 2 planes are the same area, then the volumes are the same.

The reason that Cavalieri’s name is associated with the estimation or measurement of volumes is due to the same type of misuse of Cavalieri’s work. In 1902, two geologists mistakenly connected Cavalieri’s theorem to volume estimation of crystals observed under the microscope. The name stuck. It’s just a misnomer.

Here is another mistake from the same online article.

In 1777, Count George Leclerc Buffon presented the Needle Problem to the Royal Academy of Sciences in Paris, France. The Needle Problem supplies the probability theory for current approaches to estimate the surface area and length of biological objects in an unbiased (accurate) manner.

The records of the RAS, the Royal Academy of Science, show that Buffon gave his presentation in 1733. His name was not Buffon. That’s another mistake in this online article. The name Buffon was a nickname. It comes from a town his ancestors bought. They owned the town and collected taxes for the King. His name was George LeClerc. None of my research shows he was a count, i.e. French royalty. That is yet another mistake.

If you look online you will see that the date 1777 is common. How did this mistake of 44 years come about? Part of it is poor research by the authors. The other part is a lack of understanding of the date. The person that discovered the work of Buffon was Crofton. He was looking over some books and came across an odd entry in a book by Buffon. In 1777 Buffon published a book on Natural History and added a number of odds and ends to the book. One of the add-ons was a paper he had written years earlier to get into the RAS. That is what the records of the RAS show. Buffon was known for adding all sorts of off topic entries into the backs of his books. Crofton recognized the importance of this work and mentioned it and the date of publication, which was 1777.

Today the date of publication is sometimes given erroneously as the date when Buffon presented the work.

In 1815 LaPlace corrected some of Buffon’s work from his 1733 paper. LaPlace did not name the person who’s work he was correcting. Another little item is that in 1736 Buffon did write his second article on the idea. Finally, in 1780 Buffon died. He had been in ill health and was not developing new ideas in the last few years of his life.

Another mistake is the following:

In 1847, the French mining engineer and geologist, Auguste Delesse, demonstrated that the expected value for the volume of an object varies in directly proportion to the observed area on a random section cut through the object. The Delesse Principle provides the basis for accurate and efficient estimation of object and regions volumes by point counting.

Delesse had a good idea. He did not demonstrate or prove. He developed an idea to estimate volume fraction. He never proved it worked. The method was so difficult to implement that the idea was for all intensive purposes never done. A major misleading suggestion is that the method of Delesse involved point counting.

The article is about as accurate in its content as articles about 2012, and claims that the ancient Egyptians lit their temples with electric bulbs. There is some semblance of truth, but the details are a mess of mistakes.

How can anyone suggest that Delesse had anything to do with point counting, or expected values?

How can anyone suggest that the Cavalieri principle deals with one object?

A fair assumption is that the other details provided are just as unreliable as the other claims. It ‘s largely made up and done with a bit of bravado.