. Godin, backward algorithm should be restricted to the implementation of the E-step of the EM algorithm and to the computation of the state profiles, while the Viterbi algorithm should not be use as a basis for estimation procedures. The proposed analysis methodology based on hidden semi-Markov chains is fully implemented in the AMAPmod software, 1997.

O. O. Aalen and E. Husebye, Statistical analysis of repeated events forming renewal processes, Statistics in Medicine, vol.13, issue.8, pp.1227-1240, 1991.
DOI : 10.1002/sim.4780100806

L. E. Baum, T. Petrie, G. Soules, and N. Weiss, A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains, The Annals of Mathematical Statistics, vol.41, issue.1, pp.164-171, 1970.
DOI : 10.1214/aoms/1177697196

J. V. Braun and H. Müller, Statistical methods for DNA sequence segmentation, Statistical Science, vol.13, issue.2, pp.142-162, 1998.
DOI : 10.1214/ss/1028905933

C. Burge and S. Karlin, Prediction of complete gene structures in human genomic DNA, Journal of Molecular Biology, vol.268, issue.1, pp.78-94, 1997.
DOI : 10.1006/jmbi.1997.0951

G. A. Churchill, Stochastic models for heterogeneous DNA sequences, Bulletin of Mathematical Biology, vol.45, issue.1, pp.79-94, 1989.
DOI : 10.1007/BF02458837

D. R. Cox, Partial likelihood, Biometrika, vol.62, issue.2, pp.269-276, 1975.
DOI : 10.1093/biomet/62.2.269

A. P. Dempster, N. M. Laird, R. , and D. B. , Maximum likelihood from incomplete data via the EM algorithm (with discussion), Journal of the Royal Statistical Society, Ser. B, vol.39, pp.1-38, 1977.

P. A. Devijver, Baum's forward-backward algorithm revisited, Pattern Recognition Letters, vol.3, issue.6, pp.369-373, 1985.
DOI : 10.1016/0167-8655(85)90023-6

J. D. Ferguson, Variable duration models for speech, Proceedings of the Symposium on the Applications of Hidden Markov Models to Text and Speech, pp.143-179, 1980.

D. R. Fredkin, R. , and J. A. , Bayesian Restoration of Single-Channel Patch Clamp Recordings, Biometrics, vol.48, issue.2, pp.427-448, 1992.
DOI : 10.2307/2532301

C. Godin, Y. Guédon, C. , and E. , Exploration of a plant architecture database with the AMAPmod software illustrated on an apple tree hybrid family, Agronomie, vol.19, issue.3-4, pp.163-184, 1999.
DOI : 10.1051/agro:19990301

URL : https://hal.archives-ouvertes.fr/hal-00885923

C. Godin, Y. Guédon, E. Costes, C. , and Y. , Measuring and analysing plants with the AMAPmod software, Plants to Ecosystems -Advances in Computational Life Sciences, pp.53-84, 1997.

P. J. Green, On the use of the EM algorithm for penalized likelihood estimation, Journal of the Royal Statistical Society, Ser. B, vol.52, pp.443-452, 1990.

Y. Guédon, Review of several stochastic speech unit models, Computer Speech & Language, vol.6, issue.4, pp.377-402, 1992.
DOI : 10.1016/0885-2308(92)90030-8

Y. Guédon, Hidden semi-Markov chains: A new tool for analyzing nonstationary discrete sequences, Proceedings of the 2nd International Symposium on Semi-Markov Models: Theory and Applications, 1998.

Y. Guédon, Computational methods for discrete hidden semi-Markov chains, Applied Stochastic Models in Business and Industry, vol.1, issue.3, pp.195-224, 1999.
DOI : 10.1002/(SICI)1526-4025(199907/09)15:3<195::AID-ASMB376>3.0.CO;2-F

Y. Guédon, D. Barthélémy, Y. Caraglio, C. , and E. , Pattern Analysis in Branching and Axillary Flowering Sequences, Journal of Theoretical Biology, vol.212, issue.4, pp.481-520, 2001.
DOI : 10.1006/jtbi.2001.2392

Y. Guédon and C. Cocozza-thivent, Explicit state occupancy modelling by hidden semi-Markov models: application of Derin's scheme, Computer Speech & Language, vol.4, issue.2, pp.167-192, 1990.
DOI : 10.1016/0885-2308(90)90003-O

G. Kitagawa, Non-gaussian state-space modeling of nonstationary time series (with discussion), Journal of the American Statistical Association, vol.82, pp.1032-1063, 1987.

V. G. Kulkarni, Modeling and Analysis of Stochastic Systems, 1995.

S. E. Levinson, Continuously variable duration hidden Markov models for automatic speech recognition, Computer Speech & Language, vol.1, issue.1, pp.29-45, 1986.
DOI : 10.1016/S0885-2308(86)80009-2

A. V. Lukashin and M. Borodovsky, GeneMark.hmm: new solutions for gene finding, Nucleic Acids Research, vol.26, issue.4, pp.1107-1115, 1998.
DOI : 10.1093/nar/26.4.1107

I. L. Macdonald and W. Zucchini, Hidden Markov and Other Models for Discrete-valued Time Series, 1997.

A. B. Poritz, Hidden Markov models: a guided tour, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing, pp.7-13, 1988.
DOI : 10.1109/ICASSP.1988.196495

L. R. Rabiner, A tutorial on hidden Markov models and selected applications in speech recognition, Proceedings of the IEEE, vol.77, issue.2, pp.257-286, 1989.
DOI : 10.1109/5.18626

M. J. Russell, M. , and R. K. , Explicit modelling of state occupancy in hidden Markov models for automatic speech recognition, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing, pp.5-8, 1985.
DOI : 10.1109/ICASSP.1985.1168477