A Short Diversion on Models in Science

• In the previous exercise, we made a generative model, that allowed us to make mock data and compare it with real data until the datasets matched.

• A model is good if it is able to reproduce the data: we learn by adjusting our models in the light of new information.

• The model then provides form to our understanding of the physical object. All of your understanding of everything you know about is in terms of a model.

What makes a good model?

• Models are of central importance in science: without data we have no information, and without models we have no understanding.

• Sometimes results are described as being "model-independent"; the only model-independent quantities are the data, handed to us as constants, or summaries of those data. Any physical interpretation of those data will necessarily be model-dependent.

• What people sometimes mean by "model-independent" is that their model is not simply-parameterized, and/or does not involve strong assumptions. But beware: aspiring to model-independence can lead you to overlook the assumptions that are inevitably involved.

• In general, it's best to own your model - and test your assumptions.

Models in Astrophysics

Just add parameters:

• Exponential Disk surface brightness: $x$, $y$, $R_{\rm d}$, $I_{\rm d}$

• Sersic Bulge surface brightness: $R_{\rm b}$, $I_{\rm b}$, $n_{\rm b}$

• NFW dark matter halo: $x_{\rm h}$, $y_{\rm h}$, $M_{200}$, $c_{200}$

• Mass-to-light ratios: $\mu_{\rm d}$, $\mu_{\rm b}$

and so on.