=================================================================== RCS file: /home/cvs/OpenXM/src/hgm/doc/ref-hgm.html,v retrieving revision 1.1 retrieving revision 1.4 diff -u -p -r1.1 -r1.4 --- OpenXM/src/hgm/doc/ref-hgm.html 2014/03/24 06:43:55 1.1 +++ OpenXM/src/hgm/doc/ref-hgm.html 2014/03/24 21:03:55 1.4 @@ -12,7 +12,7 @@ the Holonomic Gradient Descent Method (HGD)

Papers and Tutorials

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  1. T.Koyama, +
  2. T.Koyama, Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra, arxiv:1311.6905 @@ -30,11 +30,16 @@ T.Hibi et al, Groebner Bases : Statistics and Software Introduction to the Holonomic Gradient Method (movie), 2013. movie at youtube +
  3. T.Sei, A.Kume, -Calculating the normalising constant of the Bingham distribution on the sphere using the holonomic gradient method, +Calculating the Normalising Constant of the Bingham Distribution on the Sphere using the Holonomic Gradient Method, Statistics and Computing, 2013, DOI +
  4. T.Koyama, A.Takemura, +Calculation of Orthant Probabilities by the Holonomic Gradient Method, + arxiv:1211.6822 +
  5. T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, Holonomic Rank of the Fisher-Bingham System of Differential Equations, @@ -73,11 +78,26 @@ Advances in Applied Mathematics 47 (2011), 639--658, DOI
+

Three Steps of HGM

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  1. Find a holonomic system satisfied by the normalizing constant. +We may use computational or theoretical methods to find it. +Groebner basis and related methods are used. +
  2. Find an initial value vector for the holonomic system. +This is equivalent to evaluating the normalizing constant and its derivatives +at a point. +This step is usually performed by a series expansion. +
  3. Solve the holonomic system numerically. We use several methods +in numerical analysis such as the Runge-Kutta method of solving +ordinary differential equations and efficient solvers of systems of linear +equations. +
+

Software Packages for HGM

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  1. hgm package for R +
  2. hgm package for R for the step 3.
  3. yang (for Pfaffian systems) , nk_restriction (for D-module integrations), -tk_jack (for Jack polynomials) are in the +tk_jack (for Jack polynomials) are for the steps 1 or 2 and in the asir-contrib
@@ -86,6 +106,6 @@ tk_jack (for Jack polynomials) are in the
  • d-dimensional Fisher-Bingham System -
     $OpenXM$ 
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     $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.3 2014/03/24 07:54:51 takayama Exp $