scholarly journals A Bayesian Estimation and Predictionof Gompertz Extension Distribution Using the MCMC Method

2020 ◽  
Vol 19 (1) ◽  
pp. 142-160
Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Real Data ◽  
Simulation Method ◽  
Mcmc Methods ◽  
Mcmc Method ◽  
Data Set ◽  
Bayes Estimates ◽  
Check Method

 In this paper, the Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of the Gompertz extension distribution based on a complete sample. We have developed a procedure to obtain Bayes estimates of the parameters of the Gompertz extension distribution using Markov Chain Monte Carlo (MCMC) simulation method in OpenBUGS, established software for Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. We have obtained the Bayes estimates of the parameters, hazard and reliability functions, and their probability intervals are also presented. We have applied the predictive check method to discuss the issue of model compatibility. A real data set is considered for illustration under uniform and gamma priors.  

scholarly journals A Study of Perks-II Distribution via Bayesian Paradigm

Pravaha ◽  
2018 ◽  
Vol 24 (1) ◽  
pp. 1-17
Author(s):  
A. K. Chaudhary
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Analysis ◽  
Real Data ◽  
Simulation Method ◽  
Mcmc Methods ◽  
Data Set ◽  
Bayesian Paradigm ◽  
Mcmc Simulation

In this paper, the Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of Perks-II distribution based on a complete sample. The procedures are developed to perform full Bayesian analysis of the Perks-II distributions using Markov Chain Monte Carlo (MCMC) simulation method in OpenBUGS, established software for Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. We have obtained the Bayes estimates of the parameters, hazard and reliability functions, and their probability intervals are also presented. We have also discussed the issue of model compatibility for the given data set. A real data set is considered for illustration under gamma sets of priors.PravahaVol. 24, No. 1, 2018,page: 1-17 

scholarly journals A Bayesian Analysis of Perks Distribution via Markov Chain Monte Carlo Simulation

2013 ◽  
Vol 14 (1) ◽  
pp. 153-166 ◽  
Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Analysis ◽  
Real Data ◽  
Simulation Method ◽  
Complete Sample ◽  
Data Set ◽  
Mcmc Simulation ◽  
The Given

In this paper the Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of Perks distribution based on a complete sample. The procedures are developed to perform full Bayesian analysis of the Perks distributions using MCMC simulation method in OpenBUGS. We obtained the Bayes estimates of the parameters, hazard and reliability functions, and their probability intervals are also presented. We also discussed the issue of model compatibility for the given data set. A real data set is considered for illustration under gamma sets of priors. Nepal Journal of Science and Technology Vol. 14, No. 1 (2013) 153-166 DOI: http://dx.doi.org/10.3126/njst.v14i1.8936

scholarly journals Bayesian Analysis of Two Parameter Complementary Exponential Power Distribution

NCC Journal ◽  
2018 ◽  
Vol 3 (1) ◽  
pp. 1-23
Author(s):  
A. K. Chaudhary
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Analysis ◽  
Power Distribution ◽  
Real Data ◽  
Mcmc Methods ◽  
Output Analysis ◽  
Data Set ◽  
Exponential Power Distribution

In this paper, the Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of CEP distribution based on a complete sample. A procedure is developed to obtain Bayes estimates of the parameters of the CEP distribution using Markov Chain Monte Carlo (MCMC) simulation method in OpenBUGS, established software for Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. The MCMC methods have been shown to be easier to implement computationally, the estimates always exist and are statistically consistent, and their probability intervals are convenient to construct. The R functions are developed to study the statistical properties, model validation and comparison tools of the distribution and the output analysis of MCMC samples generated from OpenBUGS. A real data set is considered for illustration under uniform and gamma sets of priors. NCC Journal Vol. 3, No. 1, 2018,   Page: 1-23

scholarly journals Measuring Stellar Radial Velocity using Markov Chain Monte Carlo(MCMC) Method

2013 ◽  
Vol 9 (S298) ◽  
pp. 441-441
Author(s):  
Yihan Song ◽  
Ali Luo ◽  
Yongheng Zhao
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Probability Distribution ◽  
Radial Velocity ◽  
Mcmc Methods ◽  
Mcmc Method ◽  
Stellar Spectra ◽  
Mcmc Simulation ◽  
Template Fitting

AbstractStellar radial velocity is estimated by using template fitting and Markov Chain Monte Carlo(MCMC) methods. This method works on the LAMOST stellar spectra. The MCMC simulation generates a probability distribution of the RV. The RV error can also computed from distribution.

scholarly journals IMPLEMENTASI METODE MARKOV CHAIN MONTE CARLO DALAM PENENTUAN HARGA KONTRAK BERJANGKA KOMODITAS

2015 ◽  
Vol 4 (3) ◽  
pp. 122
Author(s):  
PUTU AMANDA SETIAWANI ◽  
KOMANG DHARMAWAN ◽  
I WAYAN SUMARJAYA
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Simulation Method ◽  
Commodity Price ◽  
Future Contract ◽  
Mcmc Method ◽  
Futures Contract ◽  
Mcmc Simulation ◽  
Hit And Run

The aim of the research is to implement Markov Chain Monte Carlo (MCMC) simulation method to price the futures contract of cocoa commodities. The result shows that MCMC is more flexible than Standard Monte Carlo (SMC) simulation method because MCMC method uses hit-and-run sampler algorithm to generate proposal movements that are subsequently accepted or rejected with a probability that depends on the distribution of the target that we want to be achieved. This research shows that MCMC method is suitable to be used to simulate the model of cocoa commodity price movement. The result of this research is a simulation of future contract prices for the next three months and future contract prices that must be paid at the time the contract expires. Pricing future contract by using MCMC method will produce the cheaper contract price if it compares to Standard Monte Carlo simulation.

Multimodal Markov chain Monte Carlo method for nonlinear petrophysical seismic inversion

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. M1-M13 ◽  
Author(s):  
Leandro Passos de Figueiredo ◽  
Dario Grana ◽  
Mauro Roisenberg ◽  
Bruno B. Rodrigues
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Posterior Distribution ◽  
Seismic Inversion ◽  
Forward Model ◽  
Model Parameters ◽  
Petrophysical Properties ◽  
Mcmc Method ◽  
Data Set

One of the main objectives in the reservoir characterization is estimating the rock properties based on seismic measurements. We have developed a stochastic sampling method for the joint prediction of facies and petrophysical properties, assuming a nonparametric mixture prior distribution and a nonlinear forward model. The proposed methodology is based on a Markov chain Monte Carlo (MCMC) method specifically designed for multimodal distributions for nonlinear problems. The vector of model parameters includes the facies sequence along the seismic trace as well as the continuous petrophysical properties, such as porosity, mineral fractions, and fluid saturations. At each location, the distribution of petrophysical properties is assumed to be multimodal and nonparametric with as many modes as the number of facies; therefore, along the seismic trace, the distribution is multimodal with the number of modes being equal to the number of facies power the number of samples. Because of the nonlinear forward model, the large number of modes and as a consequence the large dimension of the model space, the analytical computation of the full posterior distribution is not feasible. We then numerically evaluate the posterior distribution by using an MCMC method in which we iteratively sample the facies, by moving from one mode to another, and the petrophysical properties, by sampling within the same mode. The method is extended to multiple seismic traces by applying a first-order Markov chain that accounts for the lateral continuity of the model properties. We first validate the method using a synthetic 2D reservoir model and then we apply the method to a real data set acquired in a carbonate field.

scholarly journals Mapping-Linked Quantitative Trait Loci Using Bayesian Analysis and Markov Chain Monte Carlo Algorithms

Genetics ◽  
1997 ◽  
Vol 146 (2) ◽  
pp. 735-743 ◽  
Author(s):  
Pekka Uimari ◽  
Ina Hoeschele
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Allele Frequencies ◽  
Mcmc Methods ◽  
Substitution Effects ◽  
Indicator Variable ◽  
Trait Loci

A Bayesian method for mapping linked quantitative trait loci (QTL) using multiple linked genetic markers is presented. Parameter estimation and hypothesis testing was implemented via Markov chain Monte Carlo (MCMC) algorithms. Parameters included were allele frequencies and substitution effects for two biallelic QTL, map positions of the QTL and markers, allele frequencies of the markers, and polygenic and residual variances. Missing data were polygenic effects and multi-locus marker-QTL genotypes. Three different MCMC schemes for testing the presence of a single or two linked QTL on the chromosome were compared. The first approach includes a model indicator variable representing two unlinked QTL affecting the trait, one linked and one unlinked QTL, or both QTL linked with the markers. The second approach incorporates an indicator variable for each QTL into the model for phenotype, allowing or not allowing for a substitution effect of a QTL on phenotype, and the third approach is based on model determination by reversible jump MCMC. Methods were evaluated empirically by analyzing simulated granddaughter designs. All methods identified correctly a second, linked QTL and did not reject the one-QTL model when there was only a single QTL and no additional or an unlinked QTL.

scholarly journals Inferences for Weibull parameters under progressively first-failure censored data with binomial random removals

2020 ◽  
Vol 9 (1) ◽  
pp. 47-60
Author(s):  
Samir K. Ashour ◽  
Ahmed A. El-Sheikh ◽  
Ahmed Elshahhat
Keyword(s):  
Monte Carlo ◽  
Censored Data ◽  
Real Data ◽  
Unknown Parameters ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Squared Error Loss Function ◽  
Bayes Estimates ◽  
Monte Carlo Techniques ◽  
Credible Intervals

In this paper, the Bayesian and non-Bayesian estimation of a two-parameter Weibull lifetime model in presence of progressive first-failure censored data with binomial random removals are considered. Based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators, two-sided approximate confidence intervals for the unknown parameters are constructed. Using gamma conjugate priors, several Bayes estimates and associated credible intervals are obtained relative to the squared error loss function. Proposed estimators cannot be expressed in closed forms and can be evaluated numerically by some suitable iterative procedure. A Bayesian approach is developed using Markov chain Monte Carlo techniques to generate samples from the posterior distributions and in turn computing the Bayes estimates and associated credible intervals. To analyze the performance of the proposed estimators, a Monte Carlo simulation study is conducted. Finally, a real data set is discussed for illustration purposes.

Markov Chain Monte Carlo-Based Estimation of Stress–Strength Reliability Parameter for Generalized Linear Failure Rate Distributions

2021 ◽  
pp. 2150031
Author(s):  
F. Shahsanaei ◽  
A. Daneshkhah
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Failure Rate ◽  
Interval Estimate ◽  
Reliability Parameter ◽  
Bayes Estimates ◽  
Squared Error ◽  
Classical Inference ◽  
Strength Models

This paper provides Bayesian and classical inference of Stress–Strength reliability parameter, [Formula: see text], where both [Formula: see text] and [Formula: see text] are independently distributed as 3-parameter generalized linear failure rate (GLFR) random variables with different parameters. Due to importance of stress–strength models in various fields of engineering, we here address the maximum likelihood estimator (MLE) of [Formula: see text] and the corresponding interval estimate using some efficient numerical methods. The Bayes estimates of [Formula: see text] are derived, considering squared error loss functions. Because the Bayes estimates could not be expressed in closed forms, we employ a Markov Chain Monte Carlo procedure to calculate approximate Bayes estimates. To evaluate the performances of different estimators, extensive simulations are implemented and also real datasets are analyzed.

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