Auto-validating Samples

Overview

MRS is a C++ class library for statistical set processing.

The goal of MRS is to improve the accuracy and reliability of numerical results in computational statistical problems and provide a cohesive object-oriented framework for set-valued and set-oriented computational statistics. This is generally achieved by extending arithmetic beyond the built-in data types and applying fixed-point theorems.

MRS builds on C-XSC C eXtended for Scientific Computing and GSL Gnu Scientific Library. MRS, C-XSC and GSL are distributed under the terms of GPL, the GNU General Public License.

Download and Install

Download the source code of latest version for GNU/Linux, Linux, Unix, Mac OS X (released on 2013-03-20)

mrs-1.0.tar.gz (1.7MB), README, ChangeLog, AUTHORS, CONTENTS, COPYING, COPYRIGHT, API-Documentation (Download-Version, html-format) (10.0 MB)

Examples

MRS library provides the following features for trans-multi-dimensional inclusion-isotonic target functions:

Basic C-XSC Examples of interval arithmetic for computational statisticians
Some challenging Example target densities for optimisation and sampling
Moore Rejection Sampler for auto-validating trans-dimensional sampling
Importance sampler from pseudo and quasi random numbers
Phylogenetic posterior densities over small tree spaces
Pavings and subpavings are a set of algorithms for set processing in labeled metric spaces
Implementation of Applied Interval Analysis procedures under C-XSC -- [Jaulin et al, Springer 2001]
Adaptive histograms based on Subpavings for processing statistical sample data derived from Subpavings as a basis for statistical set processing
Automatic Differentiation for Gradients, Jacobians and Hessians (via C-XSC)
Global Optimization (multi-dimensional via C-XSC)

MRS builds upon the CXSC library that provides all features indispensable for modern numerical software development, such as

Operator concept (user-defined operators)
Overloading concept
Module concept
Dynamic arrays
Controlled rounding
Predefined arithmetic data types real, (extended real), complex, interval, complex interval, and corresponding vector and matrix types
Predefined arithmetic operators of highest accuracy for the arithmetic data types
Predefined elementary functions of highest accuracy for the arithmetic data types
Data type dotprecision for the exact representation of dot products
Library of mathematical problem-solving routines with automatic result verification and high accuracy

History

Version:: 1.0

Author:: 1. Raazesh Sainudiin (r.sainudiin ATADDRESSSYMBOL math.canterbury.ac.nz), Laboratory for Mathematical Statistical Experiments and Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand,; 2. Jennifer Harlow (jah217 ATADDRESSSYMBOL uclive.ac.nz); 3. Thomas York (tly2 ATADDRESSSYMBOL cornell.edu)

The work on MRS started during Raazesh Sainudiin's PhD dissertation. Many colleagues have contributed to the realization of MRS. See specific source files for details. Special thanks go to:

Warwick Tucker (warwick ATADDRESSSYMBOL math.uu.se) -- general advise on interval methods since 2005
Brendan Bycroft (brb44 ATADDRESSSYMBOL student.canterbury.ac.nz) -- GNU Autotools support in 2009
Gloria Teng (glo.teng ATADDRESSSYMBOL gmail.com) -- Histogram methods 2008 - 2012

References:

Posterior expectation of regularly paved random histograms, Raazesh Sainudiin, Gloria Teng, Jennifer Harlow and Dominic Lee, ACM Trans. Model. Comput. Simul. 23, 1, Article 6, 20 pages, 2013 (PDF 1864KB)
Mapped Regular Pavings, Jennifer Harlow, Raazesh Sainudiin and Warwick Tucker, Reliable Computing, vol. 16, pp. 252-282, 2012 (PDF 972KB)
Statistical regular pavings to analyze massive data of aircraft trajectories, Gloria Teng, Kenneth Kuhn and Raazesh Sainudiin, Journal of Aerospace Computing, Information, and Communication, Vol. 9, No. 1, pp. 14-25, 2012 (PS 31MB or lossy PDF 2.9MB or 26 PNG pages)
Auto-validating von Neumann Rejection Sampling from Small Phylogenetic Tree Spaces, Raazesh Sainudiin and Thomas York (PDF 1.1MB).[older version: December 2006, arXiv/math.ST/0612819 (arXiv link)], Algorithms for Molecular Biology 2009, 4:1 (Open Acess -- with sketchy latex support of the online versions as of April 25, 2009.)
Applications of interval methods to phylogenetics, Raazesh Sainudiin and Ruriko Yoshida, In L. Pachter and B. Sturmfels (Eds.), Algebraic Statistics for Computational Biology, Cambridge University Press, 2005, DOI: 10.2277/0521857007, (Cambridge Catalogue).
Enclosing the Maximum Likelihood of the Simplest DNA Model Evolving on Fixed Topologies: Towards a Rigorous Framework for Phylogenetic Inference, Raazesh Sainudiin, BSCB Dept. Technical Report BU-1653-M, Cornell University, Ithaca, New York, USA, February 2004 (revised December 2004) (PDF 1.7MB).
Machine Interval Experiments, Raazesh Sainudiin, Ph.D. dissertation in the field of Statistics, Cornell University, Ithaca, New York, USA, May 2005 (PDF 1.8MB).
An Auto-validating Rejection Sampler, Raazesh Sainudiin and Thomas York, BSCB Dept. Technical Report BU-1661-M, Cornell University, Ithaca, New York, USA, December 2005 (PDF 1.7MB).

Acknowledgements

The following sources of funding have supported past and current versions of MRS library:

2003 by NSF grant DGE-9870631 (United States)
2004, 2005 by joint NSF/NIGMS grant DMS-02-01037 (United States)
2006, 2007 by Research Fellowship of the Royal Commission for the Exhibition of 1851 (United Kingdom)
2007, 2008 by internal research grants from Mathematics and Statistics Department, University of Canterbury (New Zealand)
2009 by statistical consulting revenues of Raazesh Sainudiin
2012 University of Canterbury Postgraduate Scholarship

GNU Free Documentation License

Copyright (C) 2008, 2009, 2010, 2011, 2012, 2013 Razesh Sainudiin and Jennifer Harlow. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".