In this part I will try to explain several key issues in data analysis and statistics with the use of explicit examples and numerical codes. Most of the following material is intended for master and fledgling PhD students who want to understand the basics of data analysis with a focus on cosmology and want to enter the world of research. However, some of the examples might be a bit more advanced...
Note: for my CMB part of the CoAv course, go here.
My GitHub repository can be found here https://github.com/snesseris.
My new RSD growth-rate likelihood for Montepython can be found at my GitHub repository RSD-growth.
Prerequisites:
1) Study Chapter 15 of Numerical Recipes regarding data-fitting, minimization, MCMC, statistics etc [1], see also [2].
2) Download the Mathematica codes found below and that illustrate several key issues, like minimization and basic statistical analysis, contours, MCMC, Fourier analysis, parallelization (CPU/GPU) etc.
3) Get CAMB from here and follow the instructions in the Readme to compile and install it. Gfortran 4.5+ is highly recommended.
4) Run the codes and try to understand what's going on and most importantly why.
Numerical codes: (right-click on "Download" and hit "Save as")
1a) Statistical Significance and Sigmas. Download.
1b) The Figure of Merit (FoM). Download.
2a) Stuff about covariance matrices. Download.
2b) Marginalization of block covariance matrices. Download.
2c) The large N limit of the Poisson distribution (-> Gaussian). Download.
3a) Data fitting, contours, error bars etc. Download.
3b) Contours from empirical distribution, eg an MCMC etc. Download.
4) Generic Markov Chain Monte Carlo (MCMC). Download.
5) Generic Markov Chain Monte Carlo v2 (MCMC). Download.
6a) Bootstrap Monte Carlo. Download.
6b) Explaining the 1/e percentage replacement rule of the Bootstrap. Download.
7) The Jack-knife [3]. Download.
8a) Genetic Algorithms v1 [4]. (obsolete)
8b) Genetic Algorithms v2 [9]. Download.
9) A Mathematica Interface for CosmoMC, go here.
10a) Fitting the Union 2.1 SnIa data (standard) [5] Download.
10b) Fitting the Union 2.1 SnIa data (ultra-fast) [5] Download.
10c) Fitting the JLA SnIa data (7zip format) [6] Download.
10d) Fitting the Pantheon SnIa data [7] Download.
11) Joint SnIa, CMB, BAO and growth-rate likelihood! (ultra-fast) Download.
12) Parallelization CPU/GPU examples(coming soon).
13) The CMB power spectrum and the cosmological parameters; the correlation function (no RSD) Download.
14) The spectrum of the Gravitational Wave (GW) emission from a hyperbolic orbit. Read the paper and download the codes here.
15) The website of the Effective Fluid CLASS (EFCLASS) code, based on the papers [7] and [8], can be found here.
Note 1: Mathematica 11+ is recommended, but probably older versions will work as well.
Note 2: The Genetic Algorithms code might have some memory issues under Mathematica 9, in some systems.
Other cool stuff:
1) The sound visualized in Mathematica and a measurement of g, here.
2) How NDSolve works (also illustrates Dynamic and StepMonitor). Download
3) How ContourPlot works (also illustrates Dynamic and EvaluationMonitor). Download.
4) How FindMinimum works (also illustrates EvaluationMonitor). Download.
5) Slides of a talk I gave at the Discovery Center in Copenhagen (March 2011) on how the ancient Greek astronomers measured the distance to the Sun. Download.
6) The area of an ellipsoid. Download
References:
[1] Numerical Recipes: The Art of Scientific Computing, Third Edition (2007). Details
[2] Is the Jeffreys' scale a reliable tool for Bayesian model comparison in cosmology? arXiv:1210.7652
[3] B. Efron, The jackknife, the bootstrap, and other resampling plans, In Society of Industrial and Applied Mathematics CBMS-NSF Monographs, 38, (1982).
[4] A new perspective on Dark Energy modeling via Genetic Algorithms , arXiv:1205.0364
[5] Comparison of Recent SnIa datasets, arXiv:0908.2636
[6] Testing Einstein's gravity and dark energy with growth of matter perturbations: Indications for new Physics?, arXiv:1610.00160
[7] Unraveling the effective fluid approach for f(R) models in the subhorizon approximation, arXiv:1811.02469
[8] Designing Horndeski and the effective fluid approach, arXiv:1904.06294
[9] What can Machine Learning tell us about the background expansion of the Universe?, arXiv:1910.01529.
This page will be in a state of temporal flux, with lots of updates etc, so check back often!
Legal: The codes found in this page were developed by the author and they were used in various papers over the years. It should be made clear that they are provided with no warranty whatsoever and I'm in no way responsible for any loss of data, injury, harm to you or your equipment. Finally, everything is published under the GNU General Public License (GPLv3), found here.
Disclaimer: No master or Ph.D. students were harmed during the making of this site or any of its contents.