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Introduction to Data Analysis

A python notebook is available here. You need to use the Google Chrome Browser and install the chrome extension: Colaboratory Chrome App - this will enable in-browser execution of the python script.
(Back to IDL/GDL based tutorial Introduction to Data Analysis

Basic Concepts

The goal of any science is to develop a model that will allow one to predict the behaviour of any given system. A simple system may be to predict the acceleration of a falling object. All the parameters are known and the final velocity is a function only of the time. Other systems are more complex and may depend on many parameters, not all of which are known. The job is further complicated by the data which we collect which may be subject to experimental errors, both random and systematic.

Programming

Any field of science now requires a familiarity with computers and the ability to use at least one programming language. The programs in this module require the installation of GDL, a free data processing language that is available for a number of platforms from the main GDL site. A brief guide to its installation is here. GDL is an interpreted language which is well suited to data analysis and plotting. Because GDL is largely compatible with IDL, IDL tutorials are usually applicable to GDL and are available here, here and here. A library of astronomical routines are at Wayne Landsman’s site.

Types of Errors

Data points are always subject to errors and the modeling and interpretation of astronomical data is highly dependent on a proper statistical treatment of the data and the errors. Illegitimate errors are errors that are due to some mistake with the equipment, recording or computation. They will not be repeatable over the long run although they may be instrument dependent. Systematic errors are errors that are inherent in the experimental set up but which may be corrected for. If the experiment is repeated in exactly the same manner, the systematic errors will be consistent. An example is a balance where the balance pan has a weight which is not subtracted from the total. Random Errors are different each time the measurement is done, either due to instrumental uncertainty or to statistical uncertainty.

Random Numbers

Simulations are an integral part of modern astronomy but, in order to make them more realistic, we have to add experimental noise to them. In this section, we will discuss random numbers and will illustrate them with GDL commands. The commands will be in bold. Advanced comments will be in square brackets [...].

Uniform Distribution

In a uniform distribution, the probability of finding a value is the same everywhere within the range.

import numpy as np u=np.random.uniform(0,1,10000)	Uniform random array with 10,000 elements between 0 and 1. [1]]
import matplotlib.pyplot as plt x=xrange(0,10000) plt.plot(u,”.”) plt.show()	Plot the data with symbol type dot (.). The x axis is the index; the y axis is the value of u[i].