IJSTR

International Journal of Scientific & Technology Research

Home About Us Scope Editorial Board Blog/Latest News Contact Us
0.2
2019CiteScore
 
10th percentile
Powered by  Scopus
Scopus coverage:
Nov 2018 to May 2020

CALL FOR PAPERS
AUTHORS
DOWNLOADS
CONTACT

IJSTR >> Volume 8 - Issue 8, August 2019 Edition



International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616



Reversible Jump MCMC To Estimate A Piecewise Constant Model With Exponential Additive Noise

[Full Text]

 

AUTHOR(S)

Suparman

 

KEYWORDS

Bayesian, Piecewise Constant, Exponential Additive Noise, Reversible Jump MCMC.

 

ABSTRACT

Piecewise constant is a mathematical model that is often used to model data in various fields. Exponential multiplicative noise or exponential additive noise can be added in a constant piecewise model. This study aims to estimate a constant piecewise model that has exponential additive noise. The estimation of the constant piecewise model is carried out in the Bayesian framework. The prior distribution for the number of constant models, the location of the change in the constant model, the height of the constant model, and the noise variance selected. This prior distribution is combined with the probability function of the data to get the posterior distribution. The Bayes estimator for the number of constant models, the location of the change in the constant model, the height of the constant model, and the noise variance are estimated based on the posterior distribution. The Bayes estimator cannot be formulated explicitly because the number of constant models is a parameter. The reversible jump method of the Monte Carlo Markov Chain (MCMC) is proposed to determine the Bayes estimator. This study resulted in estimating the parameters of a constant piecewise model with exponential additive noise. This method can be used to estimate a constant piecewise model that has exponential noise even though the number of constant models is unknown.

 

REFERENCES

[1] X. Pang, S. Zhang, J. Gu, L. Li, B.Liu, and H. Wang, Improved L0 Gradient Minimization Alt L1 Fidelity for Image Smoothing, PLOS ONE, 2015, 1-10.
[2] D. Zivkovic, M. Steinrucken, Y.S. Song, and W. Stephan, Transition Densities and Sample Frequency Spectra of Diffusion Processes with Selection and Variable Population Size, Genetics, 2015, 601-617.
[3] J.A. Kamm, J.P. Spence, J. Chan, and Y.S. Song, Two-Locus Likelihoods Under Variable Population Size and Fine-Scale Recombination Rate Estimation, Genetics, 2016, 1381-1399.
[4] S. Nandy, C.Y. Lim, and T. Maiti, Additive model building for spatial regression, J.R.Statist. Soc.B, 2017, 779-800.
[5] Y. Hu, S. Feng, and L. Xue, Automatic Variable Selection for Partially Linear Functional Additive Model and Its Application to the Tecator Data Set, Mathematical Problems in Engineering, 2018, 1-9.
[6] R. Richardson, H.D. Tolley, W.E. Evenson, and B.M. Lunt, Accounting for measurement error in log regression models with applications to accelerated testing, PLOS ONE, 2018, 1-13.
[7] T.A. Marques, Predicting and Correcting Bias Caused by Measurement Error in Line Transect Sampling Using Multiplicative Error Models, Biometrics, 2004, 757-763.
[8] Suparman and M. Doisy, Bayesian Segmentation in Signal with Multiplicative Noise Using Reversible Jump MCMC, Telkomnika, 2018, 673-680.
[9] Z. Shi and H. Aoyama, Estimation of the Exponential Autoregressive time series model by using the genetic algorithm, Journal of Sound and Vibration, 1997, 309-321.
[10] N. Sad, On Exponential Autoregressive Time Series Models, J. Math, 1999, 97-101.
[11] L. Larbi and H. Fellag, Robust Bayesian Analysis of an Autoregressive Model with Exponential Innovations, Afr. Stat., 2016, 955-964.
[12] Suparman, A New Estimation Procedure Using A Reversible Jump MCMC Algorithm for AR Models of Exponential White Noise, International Journal of GEOMATE, 2018, 85-91.
[13] Suparman and M.S. Rusiman, Hierarchical Bayesian Estimation for Stationary Autoregressive Models Using Reversible Jump MCMC Algorithm International Journal of Engineering & Technology, 2018, 64-67.
[14] P.J. Green, Reversible Jump MCMC Computation and Bayesian Model Determination. Biometrika, 1995, 711-732.