MCMC采样技术及其在贝叶斯推断上的应用
|
摘要
后验分布是贝叶斯推理的本质,所有进一步的贝叶斯推断均可通过后验分布来完成.然而,应用统计实践中利用Bayes定理得到的后验密度经常是半共轭乃至复杂的、高维的.马氏链式蒙特卡洛(MCMC)方法为解决此问题提供了很好的思路.主要研究基于马氏链的蒙特卡洛采样技术基本算法和实现策略.
The posterior distribution is the essence of Bayesian inference,and all further Bayesian inference can be realized via posterior distribution. However,the posterior density function obtained by Bayes theorem in statistical practice is often semi-conjugate and even complex,high-dimensional. Markov chain Monte Carlo (MCMC) method provides a good idea to solve this problem. This paper mainly studies the basic algorithm and implementation strategy of Monte Carlo sampling technique based on Markov chain.
The posterior distribution is the essence of Bayesian inference,and all further Bayesian inference can be realized via posterior distribution. However,the posterior density function obtained by Bayes theorem in statistical practice is often semi-conjugate and even complex,high-dimensional. Markov chain Monte Carlo (MCMC) method provides a good idea to solve this problem. This paper mainly studies the basic algorithm and implementation strategy of Monte Carlo sampling technique based on Markov chain.
引文
[1]Christian Robert,Boldstad W.Understanding computational bayesian statistics[J].Chance,2012,(2):57-58.
[2]Brooks S,Gelman A,Jones G L,et al.Handbook of Markov chain Monte Carlo[J].Chance,2011,(1):53-55.
[3]Gelman,Andrew.Bayesian data analysis[M].New York:Crc Press,2012.
[4]Daphne Koller,Nir friedman.Probabilistic graphical models principles and techniques[M].Cambridge:The MIT Press,2009.
[5]Marsland S.Machine learning:An algorithmic perspective[M].Boca Raton:Chapman&Hall/CRC,2009.
[6]L.沃塞曼.统计学完全教程[M].北京:科学出版社,2008.
[7]Andrieu C,Freitas N D,Doucet A,et al.An introduction to MCMCfor machine learning[J].Machine Learning,2003,(1-2):5-43.
[8]Bolstad W M.Introduction to Bayesian Statistics[M].New Jersey:John Wiley&Sons Inc,2016.
[9]Kastner M.Monte carlo methods in statistical physics:mathematical foundations and strategies[J].Communications in Nonlinear Science&Numerical Simulation,2010,(6):1589-1602.
[10]赵琪.基于MCMC方法的贝叶斯统计推断[J].中国科技信息,2012,(10):64-65.
[11]Van Ravenzwaaij D,Cassey P,Brown S D,et al.A simple introduction to markov chain monte-carlo sampling[J].Psychonomic Bulletin&Review,2018,(1):143-154.
[2]Brooks S,Gelman A,Jones G L,et al.Handbook of Markov chain Monte Carlo[J].Chance,2011,(1):53-55.
[3]Gelman,Andrew.Bayesian data analysis[M].New York:Crc Press,2012.
[4]Daphne Koller,Nir friedman.Probabilistic graphical models principles and techniques[M].Cambridge:The MIT Press,2009.
[5]Marsland S.Machine learning:An algorithmic perspective[M].Boca Raton:Chapman&Hall/CRC,2009.
[6]L.沃塞曼.统计学完全教程[M].北京:科学出版社,2008.
[7]Andrieu C,Freitas N D,Doucet A,et al.An introduction to MCMCfor machine learning[J].Machine Learning,2003,(1-2):5-43.
[8]Bolstad W M.Introduction to Bayesian Statistics[M].New Jersey:John Wiley&Sons Inc,2016.
[9]Kastner M.Monte carlo methods in statistical physics:mathematical foundations and strategies[J].Communications in Nonlinear Science&Numerical Simulation,2010,(6):1589-1602.
[10]赵琪.基于MCMC方法的贝叶斯统计推断[J].中国科技信息,2012,(10):64-65.
[11]Van Ravenzwaaij D,Cassey P,Brown S D,et al.A simple introduction to markov chain monte-carlo sampling[J].Psychonomic Bulletin&Review,2018,(1):143-154.