116 lines
3.6 KiB
Markdown
116 lines
3.6 KiB
Markdown
# Statistical analysis
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## Description
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This repository contains the source code of two documents
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- `lectures`: a summary of the lectures of the course
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- `notes`: an explanation of the solutions of the exercises
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and the programs written for each exercise (`ex-n` directories)
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## Building the documents
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The two documents `excercise.pdf` and `lectures.pdf` are written in Pandoc
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markdown. XeTeX (with some standard LaTeX packages), the
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[pandoc-crossref](https://github.com/lierdakil/pandoc-crossref) filter and a
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Make program are required to build. Simply typing `make` in the respective
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directory will build the document, provided the above dependencies are met.
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## Building the programs
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The programs used to solve the exercise are written in standard C99 (with the
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only exception of the `#pragma once` clause) and require the following
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libraries to build:
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- [GMP](https://gmplib.org/)
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- [GSL](https://www.gnu.org/software/gsl/)
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* [pkg-config](https://www.freedesktop.org/wiki/Software/pkg-config/)
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(build-time only)
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Additionally Python (version 3) with `numpy` and `matplotlib` is required to
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generate plots.
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For convenience a `shell.nix` file is provided to set up the build environment.
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See this [guide](https://nixos.org/nix/manual/#chap-quick-start) if you have
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never used Nix before. Running `nix-shell` in the top-level will drop you into
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the development shell.
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Once ready, invoke `make` with the program you wishes to build. For example
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$ make ex-1/bin/main
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or, to build every program of an exercise
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$ make ex-1
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To clean up the build results run
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$ make clean
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## Running the programs
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Notes:
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- Many programs generate random numbers using a PRNG that is seeded with a
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fixed value, for reproducibility. It's possible to test the program on
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different samples by changing the seed via the environment variable
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`GSL_RNG_SEED`.
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### Exercise 1
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`ex-1/bin/main` generate random numbers following the Landau distribution and
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run a series of test to check if they really belong to such a distribution.
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The size of the sample can be controlled with the argument `-n N`.
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The program outputs the result of a Kolmogorov-Smirnov test and t-tests
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comparing the sample mode, FWHM and median, in this order.
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`ex-1/bin.pdf` prints a list of x-y points of the Landau PDF to the `stdout`.
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The output can be redirected to `ex-1/pdf-plot.py` to generate a plot.
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### Exercise 2
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Every program in `ex-2` computes the best available approximation (with a given
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method) to the Euler-Mascheroni γ constant and prints[1]:
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1. the leading decimal digits of the approximate value found
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2. the exact decimal digits of γ
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3. the absolute difference between the 1. and 2.
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[1]: Some program may also print additional debugging information.
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`ex-2/bin/fancy`, `ex-2/bin/fancier` can compute γ to a variable precision and
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take therefore the required number of decimal places as their only argument.
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The exact γ digits (used in comparison) are limited to 50 and 500 places,
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respectively.
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### Exercise 3
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`ex-3/bin/main` generates a sample of particle decay events and attempts to
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recover the distribution parameters via both a MLE and a χ² method. In both
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cases the best fit and the parameter covariance matrix are printed.
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The program then performs a t-test to assert the compatibility of the data with
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two hypothesis and print the results in a table.
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To plot a 2D histogram of the generated sample do
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$ ex-3/bin/main -i | ex-3/plot.py
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In addition the program accepts a few more parameters to control the histogram
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and number of events, run it with `-h` to see their usage.
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Note: the histogram parameters affect the computation of the χ² and the
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relative parameter estimation.
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