**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30526

##### Segmentation of Piecewise Polynomial Regression Model by Using Reversible Jump MCMC Algorithm

**Authors:**
Suparman

**Abstract:**

Piecewise polynomial regression model is very flexible model for modeling the data. If the piecewise polynomial regression model is matched against the data, its parameters are not generally known. This paper studies the parameter estimation problem of piecewise polynomial regression model. The method which is used to estimate the parameters of the piecewise polynomial regression model is Bayesian method. Unfortunately, the Bayes estimator cannot be found analytically. Reversible jump MCMC algorithm is proposed to solve this problem. Reversible jump MCMC algorithm generates the Markov chain that converges to the limit distribution of the posterior distribution of piecewise polynomial regression model parameter. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of piecewise polynomial regression model.

**Keywords:**
Segmentation,
Bayesian,
piecewise,
reversible Jump MCMC

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1124059

**References:**

[1] D.N. Stewart and K.A. Whaler, Optimal Piecewise Regression Analysis and Its Application to Geomagnetic Time Series, Geophysical Journal International, 1995, 710-724.

[2] H.-Y. Shi, H.-H. Lee, M.-H. Tsai, C.-C. Chiu, Y.-H. Uen and K.-T. Lee, Long-term outcomes of laparoscopic cholecystectomy: a prospective piecewise linear regression analysis, Surg Endosc, 2011, 2132-2140.

[3] J.D. Toms and M.L. Lesperance, Piecewise Regression: A Tool Identifying Ecological Thresholds, Ecology, 2003, 2034-2041.

[4] M. Tarabichi, V. Detours, and T. Konopka. Piecewise Polynomial Representations of Genome Data, Plos One, 2012, 1-10.

[5] C.P. Robert, The Bayesian Choice: A Decision-Theory Motivation, Springer, New York, 2001.

[6] P.J. Green, Reversible Jump MCMC Computation and Bayesian Model Determination, Biometrika, 1995, 711-732.

[7] Suparman and M. Doisy. Bayesian Segmentation of Piecewise Linear Regression Models Using Reversible Jump MCMC Algorithm, Computer Technology and Application, 2014, 14-18.

[8] Suparman, M. Doisy, J.Y. Tourneret, Changepoint Detection Using Reversible Jump MCMC Methods, Proceedings of IEEE ICASSP, 2002, pp. 159-1573.

[9] C.P. Robert, G. Casella, Monte Carlo Statistical Methods, Springer, New York, 1999.

[10] E. Punskaya, C. Andrieu, A. Doucet, and W.J. Fitzgerald. Bayesian Curva Fitting Using MCMC with Applications to Signal Segmentation, IEEE Transactions on Signal Processing, 2002, 747-758.