=================================================================== RCS file: /home/cvs/OpenXM/src/hgm/doc/ref-hgm.html,v retrieving revision 1.10 retrieving revision 1.23 diff -u -p -r1.10 -r1.23 --- OpenXM/src/hgm/doc/ref-hgm.html 2014/05/16 11:30:31 1.10 +++ OpenXM/src/hgm/doc/ref-hgm.html 2017/07/12 01:32:58 1.23 @@ -3,7 +3,7 @@ References for HGM - + @@ -12,6 +12,89 @@ the Holonomic Gradient Descent Method (HGD)

Papers and Tutorials

    +
  1. F.H.Danufane, K.Ohara, N.Takayama, +Holonomic Gradient Method for the Distribution Function of the Largest Root of Complex Non-central Wishart Matrices, + arxiv:1707.02564 +
  2. T.Koyama, +An integral formula for the powered sum of the independent, identically and normally distributed random variables, + arxiv:1706.03989 +
  3. H.Hashiguchi, N.Takayama, A.Takemura, +Distribution of Ratio of two Wishart Matrices and Evaluation of Cumulative Probability +by Holonomic Gradient Method, + arxiv:1610.09187 + +
  4. R.Vidunas, A.Takemura, +Differential relations for the largest root distribution +of complex non-central Wishart matrices, + arxiv:1609.01799 + +
  5. S.Mano, +The A-hypergeometric System Associated with the Rational Normal Curve and +Exchangeable Structures, + arxiv:1607.03569 + +
  6. M.Noro, +System of Partial Differential Equations for the Hypergeometric Function 1F1 of a Matrix Argument on Diagonal Regions, + ACM DL + +
  7. Y.Goto, K.Matsumoto, +Pfaffian equations and contiguity relations of the hypergeometric function of type (k+1,k+n+2) and their applications, + arxiv:1602.01637 + +
  8. T.Koyama, +Holonomic gradient method for the probability content of a simplex +region +with a multivariate normal distribution, + arxiv:1512.06564 + + +
  9. N.Takayama, S.Kuriki, A.Takemura, +A-Hpergeometric Distributions and Newton Polytopes, + arxiv:1510.02269 + +
  10. G.Weyenberg, R.Yoshida, D.Howe, +Normalizing Kernels in the Billera-Holmes-Vogtmann Treespace, + arxiv:1506.00142 + +
  11. 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, + arxiv:1507.07056 + +
  12. K.Ohara, N.Takayama, +Pfaffian Systems of A-Hypergeometric Systems II --- +Holonomic Gradient Method, + arxiv:1505.02947 + +
  13. T.Koyama, +The Annihilating Ideal of the Fisher Integral, + arxiv:1503.05261 + +
  14. T.Koyama, A.Takemura, +Holonomic gradient method for distribution function of a weighted sum +of noncentral chi-square random variables, + arxiv:1503.00378 + +
  15. Y.Goto, +Contiguity relations of Lauricella's F_D revisited, + arxiv:1412.3256 + +
  16. +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. + +DOI + + +
  17. N.Marumo, T.Oaku, A.Takemura, +Properties of powers of functions satisfying second-order linear differential equations with applications to statistics, + arxiv:1405.4451 +
  18. J.Hayakawa, A.Takemura, Estimation of exponential-polynomial distribution by holonomic gradient descent arxiv:1403.7852 @@ -28,7 +111,9 @@ Holonomic Modules Associated with Multivariate Normal Pfaffian Systems of A-Hypergeometric Equations I, Bases of Twisted Cohomology Groups, arxiv:1212.6103 -(major revision v2 of arxiv:1212.6103) +(major revision v2 of arxiv:1212.6103). +Accepted version is at + DOI
  19. Intro @@ -51,7 +136,8 @@ Calculation of Orthant Probabilities by the Holonomic
  20. T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, Holonomic Rank of the Fisher-Bingham System of Differential Equations, -to appear in Journal of Pure and Applied Algebra +Journal of Pure and Applied Algebra (online), + DOI
  21. T. Koyama, H. Nakayama, K. Nishiyama, N. Takayama, @@ -74,8 +160,8 @@ Journal of Multivariate Analysis, 116 (2013), 440--455
  22. T.Koyama, A Holonomic Ideal which Annihilates the Fisher-Bingham Integral, Funkcialaj Ekvacioj 56 (2013), 51--61. - -jstage +DOI +
  23. Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara, @@ -84,8 +170,19 @@ Holonomic Gradient Descent and its Application to Fis Advances in Applied Mathematics 47 (2011), 639--658, DOI +
+Early papers related to HGM.
+
    +
  1. +H.Dwinwoodie, L.Matusevich, E. Mosteig, +Transform methods for the hypergeometric distribution, +Statistics and Computing 14 (2004), 287--297. +
+ + +

Three Steps of HGM

  1. Finding a holonomic system satisfied by the normalizing constant. @@ -102,7 +199,13 @@ equations.

Software Packages for HGM

-Most software packages are experimental and temporary documents are found in + + + +

Programs to try examples of our papers

  1. d-dimensional Fisher-Bingham System
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