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Line 12  the Holonomic Gradient Descent Method  (HGD) </h1>
Line 14  the Holonomic Gradient Descent Method  (HGD) </h1>
   
 <h2> Papers  and Tutorials</h2>  <h2> Papers  and Tutorials</h2>
 <ol>  <ol>
   <li> M.Adamer, A.Lorincz, A.L.Sattelberger, B.Sturmfels, Algebraic Analysis of Rotation Data
   <a href="https://arxiv.org/abs/1912.00396"> arxiv: 1912.00396 </a>
   <li>
   Anna-Laura Sattelberger, Bernd Sturmfels,
   D-Modules and Holonomic Functions
   <a href="https://arxiv.org/abs/1910.01395"> arxiv:1910.01395 </a>
   <li>
   N.Takayama, L.Jiu, S.Kuriki, Y.Zhang,
   Computations of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Wishart Matrix,
   <a href="https://arxiv.org/abs/1903.10099"> arxiv:1903.10099 </a>
   <li> M.Harkonen, T.Sei, Y.Hirose,
   Holonomic extended least angle regression,
   <a href="https://arxiv.org/abs/1809.08190"> arxiv:1809.08190 </a>
   <li> S.Mano,
   Partitions, Hypergeometric Systems, and Dirichlet Processes in Statistics,
   <a href="https://www.springer.com/jp/book/9784431558866">
   JSS Research Series in Statistics</a>, 2018.
   <li> A.Kume, T.Sei,
   On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method,
   <a href="https://doi.org/10.1007/s11222-017-9765-3"> doi </a> (2018)
   <li> Yoshihito Tachibana, Yoshiaki Goto, Tamio Koyama, Nobuki Takayama,
   Holonomic Gradient Method for Two Way Contingency Tables,
   <a href="https://arxiv.org/abs/1803.04170"> arxiv:1803.04170 </a>
   <li> F.H.Danufane, K.Ohara, N.Takayama, C.Siriteanu,
   Holonomic Gradient Method-Based CDF Evaluation for the Largest Eigenvalue of a Complex Noncentral Wishart Matrix
   (Title of the version 1: Holonomic Gradient Method for the Distribution Function of the Largest Root of Complex Non-central Wishart Matrices),
   <a href="https://arxiv.org/abs/1707.02564"> arxiv:1707.02564 </a>
   <li> T.Koyama,
   An integral formula for the powered sum of the independent, identically and normally distributed random variables,
   <a href="https://arxiv.org/abs/1706.03989"> arxiv:1706.03989 </a>
   <li> H.Hashiguchi, N.Takayama, A.Takemura,
   Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability
   by Holonomic Gradient Method,
   <a href="https://arxiv.org/abs/1610.09187"> arxiv:1610.09187 </a>
   
   <li> R.Vidunas, A.Takemura,
   Differential relations for the largest root distribution
   of complex non-central Wishart matrices,
   <a href="http://arxiv.org/abs/1609.01799"> arxiv:1609.01799 </a>
   
   <li> S.Mano,
   The A-hypergeometric System Associated with the Rational Normal Curve and
   Exchangeable Structures,
   <a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a>
   
   <li> M.Noro,
   System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions,
   <a href="http://dl.acm.org/citation.cfm?doid=2930889.2930905"> ACM DL </a>
   
 <li> Y.Goto, K.Matsumoto,  <li> Y.Goto, K.Matsumoto,
 Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,  Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications,
 <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637  <a href="http://arxiv.org/abs/1602.01637"> arxiv:1602.01637 </a>
   
   <li>  T.Koyama,
   Holonomic gradient method for the probability content of a simplex
   region
   with a multivariate normal distribution,
   <a href="http://arxiv.org/abs/1512.06564">  arxiv:1512.06564 </a>
   
   
   <li> N.Takayama, S.Kuriki, A.Takemura,
   A-Hpergeometric Distributions and Newton Polytopes,
   <a href="http://arxiv.org/abs/1510.02269">  arxiv:1510.02269 </a>
   
   <li> G.Weyenberg, R.Yoshida, D.Howe,
   Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace,
   <a href="http://arxiv.org/abs/1506.00142"> arxiv:1506.00142 </a>
   
   <li> C.Siriteanu, A.Takemura, C.Koutschan, S.Kuriki, D.St.P.Richards, H.Sin,
   Exact ZF Analysis and Computer-Algebra-Aided Evaluation
   in Rank-1 LoS Rician Fading,
   <a href="http://arxiv.org/abs/1507.07056"> arxiv:1507.07056 </a>
   
   <li> K.Ohara, N.Takayama,
   Pfaffian Systems of A-Hypergeometric Systems II ---
   Holonomic Gradient Method,
   <a href="http://arxiv.org/abs/1505.02947"> arxiv:1505.02947 </a>
   
   <li> T.Koyama,
   The Annihilating Ideal of the Fisher Integral,
   <a href="http://arxiv.org/abs/1503.05261"> arxiv:1503.05261 </a>
   
   <li> T.Koyama, A.Takemura,
   Holonomic gradient method for distribution function of a weighted sum
   of noncentral chi-square random variables,
   <a href="http://arxiv.org/abs/1503.00378"> arxiv:1503.00378 </a>
   
   <li> Y.Goto,
   Contiguity relations of Lauricella's F_D revisited,
   <a href="http://arxiv.org/abs/1412.3256"> arxiv:1412.3256 </a>
   
   <li>
   T.Koyama, H.Nakayama, K.Ohara, T.Sei, N.Takayama,
   Software Packages for Holonomic Gradient Method,
   Mathematial Software --- ICMS 2014,
   4th International Conference, Proceedings.
   Edited by Hoon Hong and Chee Yap,
   Springer lecture notes in computer science 8592,
   706--712.
   <a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_105">
   DOI
   </a>
   
 <li>N.Marumo, T.Oaku, A.Takemura,  <li>N.Marumo, T.Oaku, A.Takemura,
 Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,  Properties of powers of functions satisfying second-order linear differential equations with applications to statistics,
 <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>  <a href="http://arxiv.org/abs/1405.4451"> arxiv:1405.4451</a>
Line 36  Holonomic Modules Associated with Multivariate Normal 
Line 137  Holonomic Modules Associated with Multivariate Normal 
 Pfaffian Systems of A-Hypergeometric Equations I,  Pfaffian Systems of A-Hypergeometric Equations I,
 Bases of Twisted Cohomology Groups,  Bases of Twisted Cohomology Groups,
 <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>  <a href="http://arxiv.org/abs/1212.6103"> arxiv:1212.6103 </a>
 (major revision v2 of arxiv:1212.6103)  (major revision v2 of arxiv:1212.6103).
   Accepted version is at
   <a href="http://dx.doi.org/10.1016/j.aim.2016.10.021"> DOI </a>
   
 <li> <img src="./wakaba01.png" alt="Intro">  <li> <img src="./wakaba01.png" alt="Intro">
 <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">  <a href="http://link.springer.com/book/10.1007/978-4-431-54574-3">
Line 93  Holonomic Gradient Descent  and its Application to Fis
Line 196  Holonomic Gradient Descent  and its Application to Fis
 <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a>  -->  <!-- <a href="http://arxiv.org/abs//1005.5273"> arxiv:1005.5273 </a>  -->
 Advances in Applied Mathematics 47 (2011), 639--658,  Advances in Applied Mathematics 47 (2011), 639--658,
 <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>  <a href="http://dx.doi.org/10.1016/j.aam.2011.03.001"> DOI </a>
   
 </ol>  </ol>
   
   Early papers related to HGM. <br>
   <ol>
   <li>
   H.Dwinwoodie, L.Matusevich, E. Mosteig,
   Transform methods for the hypergeometric distribution,
   Statistics and Computing 14 (2004), 287--297.
   </ol>
   
   
   
 <h2> Three Steps of HGM </h2>  <h2> Three Steps of HGM </h2>
 <ol>  <ol>
 <li> Finding a holonomic system satisfied by the normalizing constant.  <li> Finding a holonomic system satisfied by the normalizing constant.
Line 111  equations.
Line 225  equations.
 </ol>  </ol>
   
 <h2> Software Packages for HGM</h2>  <h2> Software Packages for HGM</h2>
 Most software packages are experimental and temporary documents are found in  
   <ul>
   <li>
   CRAN package <a href="https://cran.r-project.org/web/packages/hgm/index.html"> hgm </a> (for R).
   
   <li>
   Some software packages are experimental and temporary documents are found in
 "asir-contrib manual" (auto-autogenerated part), or  "asir-contrib manual" (auto-autogenerated part), or
 "Experimental Functions in Asir", or "miscellaneous and other documents"  "Experimental Functions in Asir", or "miscellaneous and other documents"
 of the  of the
Line 125  cvsweb page</a>.
Line 245  cvsweb page</a>.
 <li> Command line interfaces are in the folder OpenXM/src/hgm  <li> Command line interfaces are in the folder OpenXM/src/hgm
 in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">  in the OpenXM source tree. See <a href="http://www.math.kobe-u.ac.jp/OpenXM">
 OpenXM distribution page </a>.  OpenXM distribution page </a>.
 <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/hgm/"> hgm package for R </a> (hgm_*tar.gz, hgm-manual.pdf) for the step 3.  <li> Experimental version of <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/hgm/"> hgm package for R </a> (hgm_*tar.gz, hgm-manual.pdf) for the step 3.
 To install this package in R, type in  To install this package in R, type in
 <pre>  <pre>
 R CMD install hgm_*.tar.gz  R CMD install hgm_*.tar.gz
Line 146  maximal Likehood estimates for the Fisher-Bingham dist
Line 266  maximal Likehood estimates for the Fisher-Bingham dist
 </ul>  </ul>
 </ol>  </ol>
   
   </ul>
   
 <h2> Programs to try examples of our papers </h2>  <h2> Programs to try examples of our papers </h2>
 <ol>  <ol>
 <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>  <li> <a href="http://www.math.kobe-u.ac.jp/OpenXM/Math/Fisher-Bingham-2"> d-dimensional Fisher-Bingham System </a>
 </ol>  </ol>
   
 <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.11 2014/05/20 02:12:18 takayama Exp $ </pre>  <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.29 2019/10/31 01:53:51 takayama Exp $ </pre>
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