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Line 12  the Holonomic Gradient Descent Method  (HGD) </h1>
Line 12  the Holonomic Gradient Descent Method  (HGD) </h1>
   
 <h2> Papers  and Tutorials</h2>  <h2> Papers  and Tutorials</h2>
 <ol>  <ol>
   <li> Y.Goto, K.Matsumoto,
   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>
   
   <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> 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>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 89  Holonomic Gradient Descent  and its Application to Fis
Line 126  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 147  maximal Likehood estimates for the Fisher-Bingham dist
Line 195  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 1.10 2014/05/16 11:30:31 takayama Exp $ </pre>  <pre> $OpenXM: OpenXM/src/hgm/doc/ref-hgm.html,v 1.12 2016/02/05 01:58:34 takayama Exp $ </pre>
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