Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866915924444971008 |
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| author | Takayama, Nobuki Yaguchi, Takaharu Zhang, Yi |
| author_facet | Takayama, Nobuki Yaguchi, Takaharu Zhang, Yi |
| contents | Definite integrals with parameters of holonomic functions satisfy holonomic systems of linear partial differential equations. When we restrict parameters to a one dimensional curve, the system becomes a linear ordinary differential equation (ODE) with respect to a curve in the parameter space. We can evaluate the integral by solving the linear ODE numerically. This approach to evaluate numerically definite integrals is called the holonomic gradient method (HGM) and it is useful to evaluate several normalizing constants in statistics. We will discuss and compare methods to solve linear ODE's to evaluate normalizing constants. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2111_10947 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics Takayama, Nobuki Yaguchi, Takaharu Zhang, Yi Numerical Analysis Computation 62-8, 62E17, 65L04 Definite integrals with parameters of holonomic functions satisfy holonomic systems of linear partial differential equations. When we restrict parameters to a one dimensional curve, the system becomes a linear ordinary differential equation (ODE) with respect to a curve in the parameter space. We can evaluate the integral by solving the linear ODE numerically. This approach to evaluate numerically definite integrals is called the holonomic gradient method (HGM) and it is useful to evaluate several normalizing constants in statistics. We will discuss and compare methods to solve linear ODE's to evaluate normalizing constants. |
| title | Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics |
| topic | Numerical Analysis Computation 62-8, 62E17, 65L04 |
| url | https://arxiv.org/abs/2111.10947 |