TY - JOUR

T1 - On the reversible jump markov chain monte carlo (Rjmcmc) algorithm for extreme value mixture distribution as a location‐scale transformation of the weibull distribution

AU - Rantini, Dwi

AU - Iriawan, Nur

AU - Irhamah,

N1 - Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2021/8/2

Y1 - 2021/8/2

N2 - Data with a multimodal pattern can be analyzed using a mixture model. In a mixture model, the most important step is the determination of the number of mixture components, because finding the correct number of mixture components will reduce the error of the resulting model. In a Bayesian analysis, one method that can be used to determine the number of mixture components is the reversible jump Markov chain Monte Carlo (RJMCMC). The RJMCMC is used for distributions that have location and scale parameters or location‐scale distribution, such as the Gaussian distribution family. In this research, we added an important step before beginning to use the RJMCMC method, namely the modification of the analyzed distribution into location‐scale distribution. We called this the non‐Gaussian RJMCMC (NG‐RJMCMC) algorithm. The following steps are the same as for the RJMCMC. In this study, we applied it to the Weibull distribution. This will help many researchers in the field of survival analysis since most of the survival time distribution is Weibull. We transformed the Weibull distribution into a location‐scale distribution, which is the extreme value (EV) type 1 (Gumbel‐type for minima) distribution. Thus, for the mixture analysis, we call this EV‐I mixture distribution. Based on the simulation results, we can conclude that the accuracy level is at minimum 95%. We also applied the EV‐I mixture distribution and compared it with the Gaussian mixture distribution for enzyme, acidity, and galaxy datasets. Based on the Kullback– Leibler divergence (KLD) and visual observation, the EV‐I mixture distribution has higher coverage than the Gaussian mixture distribution. We also applied it to our dengue hemorrhagic fever (DHF) data from eastern Surabaya, East Java, Indonesia. The estimation results show that the number of mixture components in the data is four; we also obtained the estimation results of the other parameters and labels for each observation. Based on the Kullback–Leibler divergence (KLD) and visual observation, for our data, the EV‐I mixture distribution offers better coverage than the Gaussian mixture distribution.

AB - Data with a multimodal pattern can be analyzed using a mixture model. In a mixture model, the most important step is the determination of the number of mixture components, because finding the correct number of mixture components will reduce the error of the resulting model. In a Bayesian analysis, one method that can be used to determine the number of mixture components is the reversible jump Markov chain Monte Carlo (RJMCMC). The RJMCMC is used for distributions that have location and scale parameters or location‐scale distribution, such as the Gaussian distribution family. In this research, we added an important step before beginning to use the RJMCMC method, namely the modification of the analyzed distribution into location‐scale distribution. We called this the non‐Gaussian RJMCMC (NG‐RJMCMC) algorithm. The following steps are the same as for the RJMCMC. In this study, we applied it to the Weibull distribution. This will help many researchers in the field of survival analysis since most of the survival time distribution is Weibull. We transformed the Weibull distribution into a location‐scale distribution, which is the extreme value (EV) type 1 (Gumbel‐type for minima) distribution. Thus, for the mixture analysis, we call this EV‐I mixture distribution. Based on the simulation results, we can conclude that the accuracy level is at minimum 95%. We also applied the EV‐I mixture distribution and compared it with the Gaussian mixture distribution for enzyme, acidity, and galaxy datasets. Based on the Kullback– Leibler divergence (KLD) and visual observation, the EV‐I mixture distribution has higher coverage than the Gaussian mixture distribution. We also applied it to our dengue hemorrhagic fever (DHF) data from eastern Surabaya, East Java, Indonesia. The estimation results show that the number of mixture components in the data is four; we also obtained the estimation results of the other parameters and labels for each observation. Based on the Kullback–Leibler divergence (KLD) and visual observation, for our data, the EV‐I mixture distribution offers better coverage than the Gaussian mixture distribution.

KW - Bayesian analysis

KW - Location‐scale distribution

KW - Mixture distribution

KW - Reversible jump markov chain monte carlo (RJMCMC)

UR - http://www.scopus.com/inward/record.url?scp=85112573578&partnerID=8YFLogxK

U2 - 10.3390/app11167343

DO - 10.3390/app11167343

M3 - Article

AN - SCOPUS:85112573578

SN - 2076-3417

VL - 11

JO - Applied Sciences (Switzerland)

JF - Applied Sciences (Switzerland)

IS - 16

M1 - 7343

ER -