PHYS366: Statistical Methods in Astrophysics

Lesson 5: Inference in Practice: Coping With Complications Reality

Goals for this session:

• Use hierachical models to encode physical relationships among sources
• Design models that account for the imperfections of data collection
• Cope with situations where we don't know how to build a model

Related reading:

• Bits of Gelman chapters 3, 5 and 7
• Hogg et al., Data analysis recipes: Fitting a model to data

About this session

We started this course by looking at astronomical data and talking about some of its nasty features. Now that you understand the inferential tools we have at our disposal and have tested them out on relatively simple problems, it's time to get back to the dirty business of drawing conclusions from real data, warts and all.

Setting the stage

Below are three real astronomical data sets, all presenting different aspects of the "line-fit" problem we've seen before.

Question: What features can you identify in these data sets that don't fit into the simple model we've used previously?

Horizontal errors, Upper bounds only, i.e., 2d errors and non-gaussian errors - skewed errors. Not obvious that a "line" is really a good thing to try fitting. Why would thing2 vs thing1 be well-modeled by a line?

• Shape of sampling distribution
• intrinsic scatter
• outliers/interlopers
• limits/censored data
• x-errors and correlated error
• selection effects/truncated data

Let's see how we can include these features in a model. To the whiteboard!

Detour: "less probabilistic" methods