Programs and Notes

Programs:

 

GitHub: https://github.com/jjx323

 

Notes: Some notes for papers concerned with Bayesian inverse methods and inverse problems can be found on https://www.jianshu.com/u/d4eab548a4f9

 

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综述性论文:

 

1. A. M. Stuart, Inverse problems: A Bayesian perspective, Acta Numerica, 2010

2. Masoumeh Dashti and Andrew M. Stuart, The Bayesian Approach to Inverse Problem, Handbook of Uncertainty Quantification, Springer International Publishing Switzerland 2017.
3. M. Benning, M. Burger, Modern regularization methods for inverse problems, Acta Numerica, 2018
4. S. Arridge, P. Maass, O. Oktem, C. -B. Schonlieb, Solving inverse problems using data-driven models, Acta Numerica, 2019

 

阅读书目及文献:

 

统计反问题:

1. Jari Kaipio and E. Somersalo, Statistical and Computational Inverse Problems, Applied Mathematical Sciences 160, Springer, 2004.

2. T. J. Sullivan, Introduction to Uncertainty Quantification, Texts in Applied Mathematics Volume 63, Springer, 2015.

3. Masoumeh Dashti and Andrew M. Stuart, The Bayesian Approach to Inverse Problem, Handbook of Uncertainty Quantification, Springer International Publishing Switzerland 2017.

4. Evarist Gine and Richard Nickl, Mathematical Foundations of Infinite-Dimensional Statistical Models, Cambridge University Press, 2016.

 

概率论基础:

1. 程士宏,测度论与概率论基础,北京大学出版社,本科生数学基础课教材,2004.

2. Richard Durrett, Probability: Theory and Examples, Fourth Edition, Cambridge, 2010

3. Richard Durrett, Stochastic Calculus: A Practical Introduction, CRC Press 1996

 

无穷维空间上的概率测度:

1. Giuseppe Da Prato, An Introduction to Infinite-Dimensional Analysis, Springer, 2006.

2. Giuseppe Da Prato and Jerzy Zabczyk, Stochastic Equations in Infinite Dimensions, Second Edition, Cambridge University Press, 2014.

 

统计反问题计算:

1. Daniela Calvetti and Erkki Somersalo, Introduction to Bayesian Scientific Computing -- Ten Lectures on Subjective Computing, Springer, 2007.

 

泛函分析与偏微分方程等:

1. Michael Reed and Barry Simon, Methods of Modern Mathematical Physics, Volume I, Functional Analysis,Elsevier, 2003.

2. Lawrence C. Evans, Partial Differential Equations, Second Edition, American Mathematical Society, 2010.

3. Lawrence C. Evans, An Introduction to Stochastic Differential Equations,  American Mathematical Society, 2014.


机器学习:

1. Carl Edward Rasmussen and Christopher K. I. Williams, Gaussian Processes for Machine Learning, The MIT Press, Cambridge, Massachusetts, London, England, 2006.

2. Christopher M. Bishop, Pattern Recognition And Machine Learning, Springer, 2006

 

变分贝叶斯相关内容:

1. 基本的变分贝叶斯:Christopher M. Bishop, Pattern Recognition And Machine Learning, Springer, 2006 [Chapter 10]

2. Stein Variational Gradient Descent (SVGD): https://www.depthfirstlearning.com/2020/SVGD

 

采样算法(MCMC, Importance Sampling):

S. Cotter, G. Roberts, A. Stuart, D. White, MCMC methods for functions: modifying old algorithms to make them faster, Stat. Sci., 28, 2013, 424-446

 

A. Beskos, F. J. Pinski, J. M. Sanz-Serna, A. M. Stuart, Hybrid Monte Carlo on Hilbert spaces, Stochastic Processes and Their Applications, 121, 2011, 2201-2230

 

T. Bui-Thanh, O. Ghattas, J. Martin, G. Stadler, A computational framework for infinite-dimensional Bayesian inverse problems Part I: The linearized case, with application to global seismic inversion, SIAM J. Sci. Comput, 35(6), 2013, A2494-A2523

 

S. Agapiou, O. Papaspiliopoulos, D. Sanz-Alonso, A. Stuart, Importance sampling: intrinsic dimension and computational cost, Stat. Sci., 32(3), 2017, 405-431

 

K. Wang, T. Bui-Thanh, O. Ghattas, A randomized maximum a posterior method for posterior sampling of high dimensional nonlinear Bayesian inverse problems, SIAM J. Sci. Comput., 40(1), 2018, A142-A171