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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读书计划：

2021年"Mehryar Mohri, Afshin Rostamizadeh, Ameet Talwalkar, Foundations of Machine Learning, Second Edition, The MIT Press Cambridge, Massachusetts, 2018"

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综述性论文：

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

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

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. PDF

2. 严加安，测度论讲义（第二版），科学出版社，2004. 课本PDF，课后答案PDF

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

4. 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.

3. Giuseppe Da Prato, Kolmogorov Equations for Stochastic PDEs, Springer Basel AG, 2000

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)：

1. 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

 2. 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

 3. 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

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

 5. 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

注：书籍和论文可以在 http://gen.lib.rus.ec/ 上下载