Statistical analysis

Description

This repository contains the source code of two documents

• lectures: a summary of the lectures of the course

• notes: an explanation of the solutions of the exercises

and the programs written for each exercise (ex-n directories)

Building the documents

The two documents excercise.pdf and lectures.pdf are written in Pandoc markdown. XeTeX (with some standard LaTeX packages), the pandoc-crossref filter and a Make program are required to build. Simply typing make in the respective directory will build the document, provided the above dependencies are met.

Building the programs

The programs used to solve the exercise are written in standard C99 (with the only exception of the #pragma once clause) and require the following libraries to build:

• GMP

• GSL

• pkg-config (build-time only)

Additionally Python (version 3) with numpy and matplotlib is required to generate plots.

For convenience a shell.nix file is provided to set up the build environment. See this guide if you have never used Nix before. Running nix-shell in the top-level will drop you into the development shell.

Once ready, invoke make with the program you wishes to build. For example

$ make ex-1/bin/main

or, to build every program of an exercise

$ make ex-1

To clean up the build results run

$ make clean

Running the programs

Notes:

• Many programs generate random numbers using a PRNG that is seeded with a fixed value, for reproducibility. It's possible to test the program on different samples by changing the seed via the environment variable GSL_RNG_SEED.

Exercise 1

ex-1/bin/main generate random numbers following the Landau distribution and run a series of test to check if they really belong to such a distribution.
The size of the sample can be controlled with the argument -n N.
The program outputs the result of a Kolmogorov-Smirnov test and t-tests comparing the sample mode, FWHM and median, in this order.

ex-1/bin.pdf prints a list of x-y points of the Landau PDF to the stdout. The output can be redirected to ex-1/pdf-plot.py to generate a plot.

Exercise 2

Every program in ex-2 computes the best available approximation (with a given method) to the Euler-Mascheroni γ constant and prints[1]:

1. the leading decimal digits of the approximate value found

2. the exact decimal digits of γ

3. the absolute difference between the 1. and 2.

[1]: Some program may also print additional debugging information.

ex-2/bin/fancy, ex-2/bin/fancier can compute γ to a variable precision and take therefore the required number of decimal places as their only argument. The exact γ digits (used in comparison) are limited to 50 and 500 places, respectively.

Exercise 3

ex-3/bin/main generates a sample of particle decay events and attempts to recover the distribution parameters via both a MLE and a χ² method. In both cases the best fit and the parameter covariance matrix are printed.
The program then performs a t-test to assert the compatibility of the data with two hypothesis and print the results in a table.

To plot a 2D histogram of the generated sample do

$ ex-3/bin/main -i | ex-3/plot.py

In addition the program accepts a few more parameters to control the histogram and number of events, run it with -h to see their usage.

Note: the histogram parameters affect the computation of the χ² and the relative parameter estimation.