Monte Carlo Likelihood Estimation of Mixed-Effects State Space Models with Application to HIV Dynamics
Monte Carlo Likelihood Estimation of Mixed-Effects State Space Models with Application to HIV Dynamics
摘要
The statistical inference for generalized mixed-effects state space models （MESSM） are investigated when the random effects are unknown. Two filtering algorithms are designed both of which are based on mixture Kalman filter. These algorithms are particularly useful when the longitudinal ts are sparse. The authors also propose a globally convergent algorithm for parameter estimation of MESSM which can be used to locate the initial value of parameters for local while more efficient algorithms. Simulation examples are carried out which validate the efficacy of the proposed approaches. A data set from the clinical trial is investigated and a smaller mean square error is achieved compared to the existing results in literatures.
基金
supported by the National Natural Science Foundation of China under Grant No.71271165
参考文献16
-
1Liu D C, Lu T, Niu X F, et al., Mixed-effects state-space models for analysis of longitudinal dynamic systems, Biometrics, 2011, 67(2): 476-485.
-
2Chen R and Liu J S, Mixture Kalman filter, Journal of the Royal Statistical Society, Series B, 2000, 62: 493-508.
-
3Gilks W R and Berzuini C, Following a moving target-Monte Carlo inference for dynamic Baysian models, Journal of the Royal Statistical Society, Series B, 2001, 63: 127-146.
-
4Khan Z, Balch T, and Dellaert F, MCMC based particle filtering for tracking a variable number of interacting targets, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27: 1805-1819.
-
5Gilks W R, Richardson S, and Spiegelhalter D J, Markov Chain Monte Carlo in practice, Chap- man and Hall/CRC, 1996.
-
6West M, Approximating posterior distributions by mixtures, Journal of the Royal Statistical Society, Series B, 1993a, 55: 409-422.
-
7West M, Mixture models, Monte Carlo, Bayesian updating and dynamic models, Ed. by Newton J H, Computing Science and Statistics: Proceedings of the 24th Symposium on the Interface, Interface Foundation of North America, Fairfax Station, Virginia, 1993b, 325-333.
-
8Liu J S and West M, Combined parameter and state estimation in simulation-based filtering, Sequential Monte Carlo Methods in Practice editted by Doucet A, de Freitas, and Gourdon N, 2001, 197-223.
-
9Gordon N J, Salmond D J, and Smith A F M, Novel approach to nonlinear/non-Gaussian bayesian state estimation, IEEE Proceedings F, 1993, 140: 107-113.
-
10Hiirzeler M and Kiinsch H R, Approximating and Maximising the likelihood for a General state space model, Sequential Monte Carlo Methods in Practice, Eds. by Doucet A, de Freitas, and Gourdon N, 2001, 159-173.
-
1刘克.教育部颁布《中小学环境教育实施指南》[J].中国德育,2003(11):11-11. 被引量：1
-
2凌波,孙毅,陈志刚.区域竞争力系统研究[J].商场现代化,2008(11):221-221.
-
3胡振涛,Hu Yumei,Guo Zhen,Wu Yewei.Cubature Kalman probability hypothesis density filter based on multi-sensor consistency fusion[J].High Technology Letters,2016,22(4):376-384.
-
4WANG Zheng-ou Institute of Systems Engineering, Tianjin University , Tianjin, PRCZHANG Jianping Dept. of Management, Beijing Chemical Engineering College, Beijing, PRC.Modelling of a Class of Nonstationary Time Series with Kalman Filter Using Moving Window[J].Systems Science and Systems Engineering,1992,2(2):175-183.
-
5陈欣城.Hilbert—pip空间及其几何学初步[J].石家庄铁道大学学报（自然科学版）,1989,17(1):9-15.
-
6Shi XiaoKang,Wen Jun,Liu JianWen,Tian Hui,Wang Xin,Li YaoDong.Application and improvement of an adaptive ensemble Kalman filter for soil moisture data assimilation[J].Science China Earth Sciences,2010,53(11):1700-1708. 被引量：8
-
7邓自立,许燕.广义系统Wiener滤波和Kalman滤波新方法[J].控制理论与应用,1999,16(5):634-638. 被引量：6
-
8张建新,汪嘉元.徐州近百年来冷暖变化的特点[J].江苏师范大学学报（自然科学版）,1991,21(3):24-26. 被引量：1
-
9羿丹,钟海.旅行还原不物质的你[J].中外生活广场（surface）,2012(7):150-151.
-
10任敬喜,耿金花,高齐圣.多因素多指标产品的质量优化(英文)[J].山东大学学报（工学版）,2007,37(3):114-117.
