journal article Jan 01, 2013

An EM algorithm for continuous-time bivariate Markov chains

View at Publisher Save 10.1016/j.csda.2012.07.017
Topics

No keywords indexed for this article. Browse by subject →

References
35
[1]
Estimating the Infinitesimal Generator of a Continuous Time, Finite State Markov Process

Arthur Albert

The Annals of Mathematical Statistics 1962 10.1214/aoms/1177704594
[2]
Asmussen "Fitting phase-type distributions via the EM algorithm" Scand. J. Stat. (1996)
[3]
Lumpability and marginalisability for continuous-time Markov chains

Frank Ball, Geoffrey F. Yeo

Journal of Applied Probability 1993 10.2307/3214762
[4]
Statistical Inference for Probabilistic Functions of Finite State Markov Chains

Leonard E. Baum, Ted Petrie

The Annals of Mathematical Statistics 1966 10.1214/aoms/1177699147
[5]
A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains

Leonard E. Baum, Ted Petrie, George Soules et al.

The Annals of Mathematical Statistics 1970 10.1214/aoms/1177697196
[6]
Bellman (1970)
[7]
Breiman "Probability" Society for Industrial and Applied Mathematics (1992)
[8]
Breuer "An EM algorithm for batch Markovian arrival processes and its comparison to a simpler estimation procedure" Ann. Oper. Res. (2002) 10.1023/a:1020981005544
[9]
Çinlar "Markov renewal theory: A survey" Manag. Sci. (1975) 10.1287/mnsc.21.7.727
[10]
Colquhoun "On the stochastic properties of bursts of single ion channel openings and of clusters of bursts" Phil. Trans. R. Soc. Lond. B (1982) 10.1098/rstb.1982.0156
[11]
Ephraim, Y., Mark, B.L., 2012. Consistency of maximum likelihood parameter estimation for bivariate Markov chains (submitted for publication). 10.1080/15326349.2013.750534
[12]
Hidden Markov processes

Y. Ephraim, N. Merhav

IEEE Transactions on Information Theory 2002 10.1109/tit.2002.1003838
[13]
Ephraim "An EM algorithm for Markov modulated Markov processes" IEEE Trans. Signal Process. (2009) 10.1109/tsp.2008.2007919
[14]
Ferguson "Variable duration models for speech" (1980)
[15]
The Markov-modulated Poisson process (MMPP) cookbook

Wolfgang Fischer, Kathleen Meier-Hellstern

Performance Evaluation 1992 10.1016/0166-5316(93)90035-s
[16]
Freed "A Poisson process whose rate is a hidden Markov chain" Adv. Appl. Probab. (1982) 10.2307/1426731
[17]
Israel "Finding generators for Markov chains via empirical transition matrices with applications to credit ratings" Math. Finance (2001) 10.1111/1467-9965.00114
[18]
Modeling IP traffic using the batch Markovian arrival process

Alexander Klemm, Christoph Lindemann, Marco Lohmann

Performance Evaluation 2003 10.1016/s0166-5316(03)00067-1
[19]
Lancaster (1985)
[20]
Maximum-likelihood estimation for hidden Markov models

Brian G. Leroux

Stochastic Processes and their Applications 1992 10.1016/0304-4149(92)90141-c
[21]
New results on the single server queue with a batch markovian arrival process

David M. Lucantoni

Communications in Statistics. Stochastic Models 1991 10.1080/15326349108807174
[22]
Moler "Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later" SIAM Rev. (2003) 10.1137/s00361445024180
[23]
Neuts (1981)
[24]
Qin "Maximum likelihood estimation of aggregated Markov processes" Proc. Royal Society B (1997) 10.1098/rspb.1997.0054
[25]
An EM Algorithm for Ion-Channel Current Estimation

William J. J. Roberts, Yariv Ephraim

IEEE Transactions on Signal Processing 2008 10.1109/tsp.2007.906743
[26]
Roberts "On Rydén’s EM algorithm for estimating MMPPs" IEEE Signal Process. Lett. (2006) 10.1109/lsp.2006.871709
[27]
Rudemo "State Estimation for Partially Observed Markov Chains" J. Math. Anal. Appl. (1973)
[28]
Rydén "Parameter estimation for Markov modulated Poisson processes" Comm. Statist. Stochastic Models (1994) 10.1080/15326349408807323
[29]
Rydén "An EM algorithm for estimation in Markov-modulated Poisson processess" Comput. Statist. Data Anal. (1996) 10.1016/0167-9473(95)00025-9
[30]
Sohn "Stochastic analysis of exit fluid temperature records from the active TAG hydrothermal mound (Mid-Atlantic Ridge, 26°N): 2. Hidden Markov models of flow episodes" J. Geophysical Res. (2007)
[31]
Computing integrals involving the matrix exponential

C. Van Loan

IEEE Transactions on Automatic Control 1978 10.1109/tac.1978.1101743
[32]
Wei "Continuous-time hidden Markov models for network performance evaluation" Perform. Eval. (2002) 10.1016/s0166-5316(02)00122-0
[33]
Wolff (1989)
[34]
On the Convergence Properties of the EM Algorithm

C. F. Jeff Wu

The Annals of Statistics 1983 10.1214/aos/1176346060
[35]
Yu "Practical implementation of an efficient forward–backward algorithm for an explicit-duration hidden Markov model" IEEE Trans. Signal Process. (2006) 10.1109/tsp.2006.872540
Metrics
15
Citations
35
References
Details
Published
Jan 01, 2013
Vol/Issue
57(1)
Pages
504-517
License
View
Funding
U.S. National Science Foundation Award: CCF-0916568
Cite This Article
Brian L. Mark, Yariv Ephraim (2013). An EM algorithm for continuous-time bivariate Markov chains. Computational Statistics & Data Analysis, 57(1), 504-517. https://doi.org/10.1016/j.csda.2012.07.017
Related

You May Also Like

Stochastic gradient boosting

Jerome H. Friedman · 2002

5,595 citations

PLS path modeling

Michel Tenenhaus, Vincenzo Esposito Vinzi · 2005

4,750 citations

Algorithms and applications for approximate nonnegative matrix factorization

Michael W. Berry, Murray Browne · 2007

1,178 citations

Empirical characterization of random forest variable importance measures

Kellie J. Archer, Ryan V. Kimes · 2008

926 citations

Practical variable selection for generalized additive models

Giampiero Marra, Simon N. Wood · 2011

724 citations