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基于Logistic回归建模和马尔可夫链蒙特卡罗方法计算后验描述丁酸梭菌株对于给定辐照剂量区的应答趋势

周翔 姜婷婷 徐丹 杨榛 梁剑平 王亮

周翔, 姜婷婷, 徐丹, 杨榛, 梁剑平, 王亮. 基于Logistic回归建模和马尔可夫链蒙特卡罗方法计算后验描述丁酸梭菌株对于给定辐照剂量区的应答趋势[J]. 原子核物理评论, 2016, 33(4): 500-505. doi: 10.11804/NuclPhysRev.33.04.500
引用本文: 周翔, 姜婷婷, 徐丹, 杨榛, 梁剑平, 王亮. 基于Logistic回归建模和马尔可夫链蒙特卡罗方法计算后验描述丁酸梭菌株对于给定辐照剂量区的应答趋势[J]. 原子核物理评论, 2016, 33(4): 500-505. doi: 10.11804/NuclPhysRev.33.04.500
ZHOU Xiang, JIANG Tingting, XU Dan, YANG Zhen, LIANG Jianping, WANG Liang. Combining Logistic Regression and Markov Chain Monte-Carlo Describe the Relationship between Exposure to a Given Dose of Radiation and its Effect on Clostridium tyrobutyricum Strains[J]. Nuclear Physics Review, 2016, 33(4): 500-505. doi: 10.11804/NuclPhysRev.33.04.500
Citation: ZHOU Xiang, JIANG Tingting, XU Dan, YANG Zhen, LIANG Jianping, WANG Liang. Combining Logistic Regression and Markov Chain Monte-Carlo Describe the Relationship between Exposure to a Given Dose of Radiation and its Effect on Clostridium tyrobutyricum Strains[J]. Nuclear Physics Review, 2016, 33(4): 500-505. doi: 10.11804/NuclPhysRev.33.04.500

基于Logistic回归建模和马尔可夫链蒙特卡罗方法计算后验描述丁酸梭菌株对于给定辐照剂量区的应答趋势

doi: 10.11804/NuclPhysRev.33.04.500
基金项目: 中国科学院西部之光人才培养引进计划——“西部青年学者”A类项目(Ke-Fa-Ren-Zi[2015]No.77);甘肃省自然科学基金项目(1506RJZA293)
详细信息
    作者简介:

    周翔(1977-),男,兰州人,博士后,副研究员,硕士研究生导师,从事生物物理与代谢工程研究;E-mail:syannovich@gmail.com;syannovich@impcas.ac.cn

  • 中图分类号: R815.2;TL72

Combining Logistic Regression and Markov Chain Monte-Carlo Describe the Relationship between Exposure to a Given Dose of Radiation and its Effect on Clostridium tyrobutyricum Strains

Funds: CAS Light of West China Program(Ke-Fa-Ren-Zi[2015] No.77); Natural Science Foundation of Gansu Provincial(1506RJZA293)
  • 摘要: 利用马尔可夫链蒙特卡罗(Markov Chain Monte Carlo,MCMC)方法估计Logistic回归模型中的参数,就是要构造一个以参数的后验分布为其平稳分布的非周期不可约的马尔可夫链,然后用该平稳分布中抽出的样本点计算蒙特卡罗积分。上述理论方法可以解决实验样本数据由于存在定和约束和多重共线性、在进行经典的logistic回归建模时的困难问题。基于此方法,研究了丁酸梭菌株对于给定辐照区间剂量的应答趋势,用模型挖掘数据所隐含的内在信息并导出了Logistic回归模型参数的贝叶斯框架下的50%,90%,95%和99%的置信区间。结果表明,运用Logistic与马尔可夫链耦合模型在有关给定辐射剂量对于微生物作用效果问题的logistic回归建模中具有较大的科学性与很好的使用性,从而可以为辐照诱变处理微生物制定辐照剂量区提供理论支持和回归技术借鉴。


    Using the Markov Chain Monte-Carlo method to estimate the parameters in the Logistic regression model, we constructed a non-periodic irreducible Markov Chain with the posterior distribution of the parameters as stationary distribution, and then used the sample points extracted from the stationary distribution to calculate the Monte-Carlo integral. The above theoretical method can solve the difficult problem of classical logistic regression modeling because of the existence and limitation of the experimental sample data and the multicollinearity. In the classical regression setup with a continuous response, the predicted values can range over all real numbers. Therefore, a different modelling technique is needed. In this work, the results describe in detail a previously unknown lethality trend following 12C6+ heavy-ion irradiation of Clostridium tyrobutyricum. By Markov Chain Monte-Carlo can calculate the model fit for a randomly selected subset of the chain and calculate the predictive envelope of the model. The grey areas in the plot correspond to 50%, 90%, 95%, and 99% posterior regions. More importantly, although this study focused on the use of the method in heavy-ion irradiation of microbial, its results are broadly applicable.
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出版历程
  • 收稿日期:  2016-03-21
  • 修回日期:  2016-05-25
  • 刊出日期:  2016-12-20

基于Logistic回归建模和马尔可夫链蒙特卡罗方法计算后验描述丁酸梭菌株对于给定辐照剂量区的应答趋势

doi: 10.11804/NuclPhysRev.33.04.500
    基金项目:  中国科学院西部之光人才培养引进计划——“西部青年学者”A类项目(Ke-Fa-Ren-Zi[2015]No.77);甘肃省自然科学基金项目(1506RJZA293)
    作者简介:

    周翔(1977-),男,兰州人,博士后,副研究员,硕士研究生导师,从事生物物理与代谢工程研究;E-mail:syannovich@gmail.com;syannovich@impcas.ac.cn

  • 中图分类号: R815.2;TL72

摘要: 利用马尔可夫链蒙特卡罗(Markov Chain Monte Carlo,MCMC)方法估计Logistic回归模型中的参数,就是要构造一个以参数的后验分布为其平稳分布的非周期不可约的马尔可夫链,然后用该平稳分布中抽出的样本点计算蒙特卡罗积分。上述理论方法可以解决实验样本数据由于存在定和约束和多重共线性、在进行经典的logistic回归建模时的困难问题。基于此方法,研究了丁酸梭菌株对于给定辐照区间剂量的应答趋势,用模型挖掘数据所隐含的内在信息并导出了Logistic回归模型参数的贝叶斯框架下的50%,90%,95%和99%的置信区间。结果表明,运用Logistic与马尔可夫链耦合模型在有关给定辐射剂量对于微生物作用效果问题的logistic回归建模中具有较大的科学性与很好的使用性,从而可以为辐照诱变处理微生物制定辐照剂量区提供理论支持和回归技术借鉴。


Using the Markov Chain Monte-Carlo method to estimate the parameters in the Logistic regression model, we constructed a non-periodic irreducible Markov Chain with the posterior distribution of the parameters as stationary distribution, and then used the sample points extracted from the stationary distribution to calculate the Monte-Carlo integral. The above theoretical method can solve the difficult problem of classical logistic regression modeling because of the existence and limitation of the experimental sample data and the multicollinearity. In the classical regression setup with a continuous response, the predicted values can range over all real numbers. Therefore, a different modelling technique is needed. In this work, the results describe in detail a previously unknown lethality trend following 12C6+ heavy-ion irradiation of Clostridium tyrobutyricum. By Markov Chain Monte-Carlo can calculate the model fit for a randomly selected subset of the chain and calculate the predictive envelope of the model. The grey areas in the plot correspond to 50%, 90%, 95%, and 99% posterior regions. More importantly, although this study focused on the use of the method in heavy-ion irradiation of microbial, its results are broadly applicable.

English Abstract

周翔, 姜婷婷, 徐丹, 杨榛, 梁剑平, 王亮. 基于Logistic回归建模和马尔可夫链蒙特卡罗方法计算后验描述丁酸梭菌株对于给定辐照剂量区的应答趋势[J]. 原子核物理评论, 2016, 33(4): 500-505. doi: 10.11804/NuclPhysRev.33.04.500
引用本文: 周翔, 姜婷婷, 徐丹, 杨榛, 梁剑平, 王亮. 基于Logistic回归建模和马尔可夫链蒙特卡罗方法计算后验描述丁酸梭菌株对于给定辐照剂量区的应答趋势[J]. 原子核物理评论, 2016, 33(4): 500-505. doi: 10.11804/NuclPhysRev.33.04.500
ZHOU Xiang, JIANG Tingting, XU Dan, YANG Zhen, LIANG Jianping, WANG Liang. Combining Logistic Regression and Markov Chain Monte-Carlo Describe the Relationship between Exposure to a Given Dose of Radiation and its Effect on Clostridium tyrobutyricum Strains[J]. Nuclear Physics Review, 2016, 33(4): 500-505. doi: 10.11804/NuclPhysRev.33.04.500
Citation: ZHOU Xiang, JIANG Tingting, XU Dan, YANG Zhen, LIANG Jianping, WANG Liang. Combining Logistic Regression and Markov Chain Monte-Carlo Describe the Relationship between Exposure to a Given Dose of Radiation and its Effect on Clostridium tyrobutyricum Strains[J]. Nuclear Physics Review, 2016, 33(4): 500-505. doi: 10.11804/NuclPhysRev.33.04.500
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