Mathematics and Statistics Vol. 10(6), pp. 1285 - 1292
DOI: 10.13189/ms.2022.100614
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Signal Modeling with IG Noise and Parameter Estimation Based on RJMCMC

Akhmad Fauzy ¹, Suparman ^2,*, Epha Diana Supandi ^3
1 Department of Statistics, Universitas Islam Indonesia, Indonesia
² Department of Mathematics Education, Universitas Ahmad Dahlan, Indonesia
³ Department of Mathematics, Universitas Islam Negeri Sunan Kalijaga, Indonesia

ABSTRACT

Piecewise constant (PC) is a stochastic model that can be applied in various fields such as engineering and ecology. The stochastic model contains a noise. The accuracy of the stochastic model in modeling a signal is influenced by the type of noise. This paper aims to propose inverse-gamma noise in the PC model and the procedure for estimating the model parameters. The model parameters are estimated using the Bayes approach. Model parameters have a variable dimension space so that the Bayesian estimator cannot be determined analytically. Therefore, the Bayesian estimator is calculated using the reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm. The performance of the RJMCMC algorithm is validated using data synthesis. The finding is a new PC model in which the noise has an inverse-gamma distribution. In addition, this paper also proposes a parameter estimation procedure for the model based on an RJMCMC. The simulation study shows that the model parameter estimators generated by this algorithm are close to the model parameter values. This paper concludes that inverse gamma noise can be used as an alternative noise in the PC model. The RJMCMC is categorized as a valid algorithm and can estimate the PC model parameters where the noise has an inverse-gamma distribution. The novelty in this paper is the development of a new stochastic model and the procedure for estimating the model parameters. In application, the findings in this paper have the potential to improve the suitability of the stochastic model to the signal.

KEYWORDS
Bayes Methods, Inverse-gamma Noise, Monte Carlo Methods, Piecewise Constant, Signal Detection

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Akhmad Fauzy , Suparman , Epha Diana Supandi , "Signal Modeling with IG Noise and Parameter Estimation Based on RJMCMC," Mathematics and Statistics, Vol. 10, No. 6, pp. 1285 - 1292, 2022. DOI: 10.13189/ms.2022.100614.

(b). APA Format:
Akhmad Fauzy , Suparman , Epha Diana Supandi (2022). Signal Modeling with IG Noise and Parameter Estimation Based on RJMCMC. Mathematics and Statistics, 10(6), 1285 - 1292. DOI: 10.13189/ms.2022.100614.