This database tries to bring together all available information about Markov bases. Markov bases are used in algebraic statistics. From a statistical point of view they can be used to estimate the goodness of a fit of empirical data to a statistical model. In algebraic geometry Markov bases are equivalent to generating set of toric ideals. These ideas are explained in the seminal 1998 paper from P. Diaconis and B. Sturmfels^{[1]}. If you want to know how Markov bases are computed please have a look at the Theory section of the 4ti2-homepage.
At the moment the database is far from complete. We invite everybody to submit their Markov bases computations. Feel free to write us us with either of the following:
If you wish to download the whole database to run extensive statistics or your own searches, please also e-mail us to arrange the download.
Click on DATABASE or SEARCH at the top of this page to access the database. At the top of the page the database entries are shown. At the bottom a form can be used to search the database.
A click on any name in the database leads to a page that summarizes the data of any specific Markov base. On this
page there is also a list of files that contain further information. Most important, for every Markov basis in the
database there is a corresponding file with ending .mar
that contains the Markov basis itself.
All Markov bases have been computed by 4ti2. Thus the format of
the files is just the 4ti2-format (cf. the Data Structure section of
the 4ti2-homepage): Basically every file contains a matrix. The
first line contains its width and its height. If the file contains elements of a Markov basis (e.g. a
file of type .mar
or .mar.rep
), then the Markov basis elements are written as row
vectors.
For those models created with the genmodel
script provided by 4ti2 the
corresponding .mod
file is also provided. In this case, the .mod
file indicates how the
probabilities in the .mar
file are ordered.
Normality of the corresponding semigroup was checked using Normaliz.
See here for further references.
Thomas Kahle - thomas-kahle(at)gmx.de
Johannes Rauh - jarauh(at)gmx.net
This service is offered in the hope that it will be useful, but WITHOUT ANY WARRANTY (express or implied) as to the accuracy or completeness of any information provided to you.
page last update on March 29 2016. ->Contact