#### model vs model

As Alanna pointed out, astronomers and statisticians mean different things when they say “model”. To complicate matters, we have also started to use another term called “data model”.

First, there is the physical model, which could mean either our understanding of what processes operate on a source (the physics part, usually involving PDEs), or the mathematical function that describes the emission as a function of observables like location, time, or energy (the astronomy part, usually the shape of the spectrum, or the time evolution in a light curve, etc.)

The data model on the other hand describes the organization of the observation. It is this which tells us that there is a fundamental difference between an effective area and a response matrix, and conversely, that the point spread function and the line response function are the same beast. This kind of thing, which I suppose is a computer science oriented view of the contents of a file, is crucial for implementing and running something like the Virtual Observatory.

1. ##### hlee:

Due to the binary nature of data model and computer science, interpreting data model into statistical one for the inference purpose comes smoothly, in contrast to astronomers’ model. The challenges lie in developing computer scientific theories, most of which can be associated with already existing theories from mathematical statistics. However, this is not always true when it comes to Information Theory.

[Response: Hmm. I don't see how the data model can have relevance to statistical inference. It is not binary. It is essentially imposing an object-oriented approach which may help in the writing of generalized Bayesian code easier, but other than that, it doesn't have any connection to statistics. It might help to make your programs run better (maybe even faster) and be written in a more scalable fashion.
-vlk]

10-05-2007, 5:28 pm
2. ##### hlee:

I recommend a book by Thomas and Cover, Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing) and a paper by Shannon, A mathematical theory of communication. Particularly, the book is very good for general purposes (coding, data compression, signal/image processing, and filter design; I heard many CS/EE departments use this book in their required course works) and it contains quite many statistical theorems, which are the bases of developing a data model, or an object-oriented approach to write a code.

[Added] Elements of Information Theory has its own website: http://www.elementsofinformationtheory.com/ Some years ago, I was able to find many course websites that said required textbook and contained problems, solutions, and relevant research topics including one of the authors’ course website at Stanford. A personal wish is that statistics departments offer Information Theory related courses with a cross opening to astronomy students.

10-09-2007, 6:01 pm