PHYS366: Statistical Methods in Astrophysics

Lesson 2: Understanding From Data

Goals for this session:

  • Be able to describe the Bayesian view of models, parameters and uncertainty

  • Know how to set up and perform simple Bayesian inferences, including the assignment of probability distributions

  • Be able to draw simple PGMs and understand their connection to probability expressions

  • MacKay Chapter 2, sections 2.1, 2.1, 2.3, and Chapter 3, sections 3.1, 3.2
  • Ivezic Chapter 3, sections 3.1, 3.3 and Chapter 5, sections 5.1, 5.2, 5.3

Generative Models and Posterior Inferences

A good way to start understanding a dataset is to try to recreate it.

Now, let's look at the inverse problem, and learn the model parameters from the data. Along the way, we'll need to remind ourselves about probability.

Example: The Cepheid Period-Luminosity Relation

  • Let's get some more practice in setting up a Bayesian inference.
  • This boils down to two tasks: 1) assigning probability distributions (for both the data and the parameters) and 2) doing integrals.

Assigning Priors

In the previous examples, we assigned various prior PDFs for our model parameters.


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