Quantifying uncertainty in the numerical integration of evolution equations based on Bayesian isotonic regression
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917835897307136 |
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| author | Miyatake, Yuto Irie, Kaoru Matsuda, Takeru |
| author_facet | Miyatake, Yuto Irie, Kaoru Matsuda, Takeru |
| contents | This paper presents a new Bayesian framework for quantifying discretization errors in numerical solutions of ordinary differential equations. By modelling the errors as random variables, we impose a monotonicity constraint on the variances, referred to as discretization error variances. The key to our approach is the use of a shrinkage prior for the variances coupled with variable transformations. This methodology extends existing Bayesian isotonic regression techniques to tackle the challenge of estimating the variances of a normal distribution. An additional key feature is the use of a Gaussian mixture model for the $\log$-$χ^2_1$ distribution, enabling the development of an efficient Gibbs sampling algorithm for the corresponding posterior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08338 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantifying uncertainty in the numerical integration of evolution equations based on Bayesian isotonic regression Miyatake, Yuto Irie, Kaoru Matsuda, Takeru Numerical Analysis Data Analysis, Statistics and Probability Methodology This paper presents a new Bayesian framework for quantifying discretization errors in numerical solutions of ordinary differential equations. By modelling the errors as random variables, we impose a monotonicity constraint on the variances, referred to as discretization error variances. The key to our approach is the use of a shrinkage prior for the variances coupled with variable transformations. This methodology extends existing Bayesian isotonic regression techniques to tackle the challenge of estimating the variances of a normal distribution. An additional key feature is the use of a Gaussian mixture model for the $\log$-$χ^2_1$ distribution, enabling the development of an efficient Gibbs sampling algorithm for the corresponding posterior. |
| title | Quantifying uncertainty in the numerical integration of evolution equations based on Bayesian isotonic regression |
| topic | Numerical Analysis Data Analysis, Statistics and Probability Methodology |
| url | https://arxiv.org/abs/2411.08338 |