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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> Nobuki Takayama, Takaharu Yaguchi, Yi Zhang,
   Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics,
   <a href="https://arxiv.org/abs/2111.10947"> arxiv:2111.10947 </a>
   
   <li> Shuhei Mano, Nobuki Takayama,
   Algebraic algorithm for direct sampling from toric models,
   <a href="https://arxiv.org/abs/2110.14992"> arxiv:2110.14992 </a>
   
   <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> -->
   <a href="https://doi.org/10.1016/j.jmva.2020.104642"> jmva </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,  <li> H.Hashiguchi, N.Takayama, A.Takemura,
 Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability  Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability
 by Holonomic Gradient Method,  by Holonomic Gradient Method,
Line 25  of complex non-central Wishart matrices,
Line 67  of complex non-central Wishart matrices,
 <li> S.Mano,  <li> S.Mano,
 The A-hypergeometric System Associated with the Rational Normal Curve and  The A-hypergeometric System Associated with the Rational Normal Curve and
 Exchangeable Structures,  Exchangeable Structures,
   <a href="http://doi.org/10.1214/17-EJS1361"> doi </a>,
 <a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a>  <a href="http://arxiv.org/abs/1607.03569"> arxiv:1607.03569 </a>
   
   
 <li> M.Noro,  <li> M.Noro,
 System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions,  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>  <a href="http://dl.acm.org/citation.cfm?doid=2930889.2930905"> ACM DL </a>
Line 41  region
Line 85  region
 with a multivariate normal distribution,  with a multivariate normal distribution,
 <a href="http://arxiv.org/abs/1512.06564">  arxiv:1512.06564 </a>  <a href="http://arxiv.org/abs/1512.06564">  arxiv:1512.06564 </a>
   
   <li> N.Takayama, Holonomic Gradient Method (in Japanese, survey),
   <a href="http://www.math.kobe-u.ac.jp/HOME/taka/2015/hgm-dic.pdf">
   hgm-dic.pdf </a>
   
 <li> N.Takayama, S.Kuriki, A.Takemura,  <li> N.Takayama, S.Kuriki, A.Takemura,
 A-Hpergeometric Distributions and Newton Polytopes,  A-Hpergeometric Distributions and Newton Polytopes,
Line 105  Holonomic Modules Associated with Multivariate Normal 
Line 152  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 239  maximal Likehood estimates for the Fisher-Bingham dist
Line 288  maximal Likehood estimates for the Fisher-Bingham dist
 <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 1.20 2016/09/22 02:51:13 takayama Exp $ </pre>  <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.33 2021/12/13 04:40:21 takayama Exp $ </pre>
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