A Short Tour of an Astronomical Inference

Goals:

  • Understand what is meant by "data", "noise", and "models"
  • Gain some appreciation for what astronomical data is like, and what astronomers are typically trying to do

References

  • Ivezic Chapter 1, sections 1.1, 1.2, 1.4, 1.5, and Chapter 3, section 3.2.

Data analysis

  • What is data?

  • How should we think about data in science?

You probably already have an unarticulated but likely strong sense of what data is: like many other obvious things, you know it when you see it.

One of our tasks will be to define what we mean by data mathematically, but we'll start by exploring a simple example astronomical data analysis.

Where do astronomical data come from?

  • Propose observations
  • Observe sky, collect and "reduce" data
  • Explore and summarize reduced data
  • Hypothesize, and test
  • Interpret, conclude, speculate
  • Report

This course concerns the parts of the investigation in bold.

An Example Image Dataset

  • In optical, X-ray and gamma-ray astronomy, the most basic datasets are images

  • Images can be 2D, from cameras, or 1D, from spectrographs, or 3D, from IFUs (integral field units).

  • Image data come packaged as an array of numbers, which we can visualize, and do calculations with.

Let's look at some X-ray image data from the XMM satellite, for the galaxy cluster A1835.

What is "data"?

  • Data are constants (usually numbers)

  • That we are handed (typically in a data file)

  • That we hope to learn something from.

Uncertainty

Here's a zoomed in view of the central part of the A1835 XMM image:

Learning from data

  • Data analysis is central to the scientific process: statistical inference is the mathematical formalization of learning.

  • The formalism is important: hypothesizing, testing, and inteprreting are all potentially very messy.