The study of geometric probability in stereology may seem like a large, overwhelming area of focus but, don’t panic, it’s not! In fact, it is a very specific field that is likely to come easy to those that excel in mathematics or science (yes that means you). However, the concept is not one that most people can grasp, let alone learn, especially if the material is poorly communicated.
Before fully submerging into the role of geometric probability in stereology, you should first have a smattering of knowledge about geometric probability. As its name suggests, geometric probability is exactly that- it is the act of finding a probability by using geometry. You simply apply formulas, lines or planes to the given geometric figure and then use this information to answer the probability question.
The Components of Geometric Probability in Stereology
Before you can understand and apply this over-complicated discipline to your work, you need to first have a basic, clear and solid understanding of each component. Here is that information in the simplest of terms.
Math 101
At some point or other, every pupil and student learns geometry. This is the branch of mathematics which asks (and answers) questions regarding the shape, size, special properties and position of an object in relation to another. To apply geometric concepts, you must determine the height, length or width of the object in question so that you can obtain its area, diameter, circumference, volume or the distance between it and another item. It allows a researcher to apply a number to a one-dimensional object, such as a line, a two-dimensional structure, like an image or a three-dimensional item, like you!
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We live in 4D
People can also fall into the category of being four-dimensional because life occurs in the dimension of time, which is relative to motion and space. As for the zero dimension, this refers to an immeasurable point in space and time; it has no length, width, height, depth or volume. It is an infinitely small singularity that can be defined as nothing, or as a point where everything occurs in the same place. An example of such a dimension is the black hole or the period at the end of this sentence.
As a reminder, geometry also incorporates the use of graphs, linear equations, curves, planes, the compass and simple straightedge rulers, all of which are important to geometric probability in stereology.
Defining Stereology
Stereology is an area of scientific study that relies heavily on geometry, as its goal is to obtain the quantities, or numbers, of three-dimensional objects, those with a measurable height, length, and width, by using images that have only two dimensions: width and length.
Note: The method for discovering such numbers is not discussed here; instead, the focus is on the importance of finding them. Once you have the data necessary to move forward, you can use it to analyze and explain the relationship between an item’s function and its structure.
Geometric Probability in Stereology
Now that you have a simplified breakdown of each component involved in geometric probability in stereology, you are ready to take a look at the actual use of geometric probability in stereology, as well as the advantages and disadvantages of this technique.
As you’ll know from the introduction here, stereology looks at the relativity between an object and its sections, while geometric probability allows a researcher to expand their data by providing additional information.
Layman’s terms
Geometric probability in stereology studies the relationship of the object, its sections, and the factors that are independent of the object’s structure and shape. In layman’s terms, stereology and geometric probability complement each other, as the former would not be complete without the latter.
Basic formula- it’s easy!
To obtain the quantities necessary to perform a stereological study using geometric probability, you can apply a simple formula, then simply plug in the known numbers so that you obtain the unknown measurements and then solve accordingly. The most basic formula to use is:
Ev (cvV) = Ea (caA)
Ev (V) Ea (A)
- ‘V’ is the volume of the object.
- ‘A’ is the area of the object section.
- ‘cv’ is the volume composition of the object.
- ‘ca’ is the area composition of the object section.
The Ev signifies the average with respect to the object and the Ea refers to the average with regards to the object section.
Though there are other methods for conducting geometric probability in stereology, you can use this formula for just about any application, whether you are studying tissue samples, bone, mineral fragments or the brain.
Advantages and Disadvantages of Geometric Probability
Using geometric probability in stereology not only allows researchers to expand their data and perform a stereological study; it also provides unbiased results. The tools used to perform geometric probability allow for an accurate cell count and the grids help to identify outliers and determine proximity, all of which are beneficial when trying to figure out the relationship between specific objects and the space that surrounds them.
However, this does not mean the results are unbiased, as geometric probability often relies on estimates. Still, the numbers do provide important information, such as the area of a tissue that has the most cell growth, or when and where antibody penetration is least likely to occur.
Although the numbers may not be exact, they are still close enough to provide pertinent information that can help researchers analyze, learn, study, interpret, and discover new details about people, the environment, and other objects that play a key role in everyday living.
See, we told you it wasn’t scary!
This area of science and mathematics is very important to studying, analyzing, and diagnosing various specimens. If you intend on having a career that intertwines with this field, you should have a good understanding of the theories, methods, applications, and interpretation of the results so you can get involved in the process.
Overall, geometric probability in stereology is not as difficult a concept as you may have originally thought, especially once you break down the big, scary phrases into smaller pieces!
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