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 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 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 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.

Markov Chain Monte Carlo

2015 ◽  
Author(s):  
N. Thompson Hobbs ◽  
Mevin B. Hooten
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Analysis ◽  
Posterior Distribution ◽  
Mcmc Algorithm ◽  
Bayesian Analyses ◽  
Seminal Paper ◽  
Formal Treatment ◽  
High Level

This chapter explains how to implement Bayesian analyses using the Markov chain Monte Carlo (MCMC) algorithm, a set of methods for Bayesian analysis made popular by the seminal paper of Gelfand and Smith (1990). It begins with an explanation of MCMC with a heuristic, high-level treatment of the algorithm, describing its operation in simple terms with a minimum of formalism. In this first part, the chapter explains the algorithm so that all readers can gain an intuitive understanding of how to find the posterior distribution by sampling from it. Next, the chapter offers a somewhat more formal treatment of how MCMC is implemented mathematically. Finally, this chapter discusses implementation of Bayesian models via two routes—by using software and by writing one's own algorithm.

scholarly journals Multivariate output analysis for Markov chain Monte Carlo

Biometrika ◽  
2019 ◽  
Vol 106 (2) ◽  
pp. 321-337 ◽  
Author(s):  
Dootika Vats ◽  
James M Flegal ◽  
Galin L Jones
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Output Analysis

scholarly journals Markov chain Monte Carlo inference for Markov jump processes via the linear noise approximation

2013 ◽  
Vol 371 (1984) ◽  
pp. 20110541 ◽  
Author(s):  
Vassilios Stathopoulos ◽  
Mark A. Girolami
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Jump Processes ◽  
Mcmc Methods ◽  
Computationally Efficient ◽  
Markov Jump ◽  
Riemann Manifold ◽  
Exact Inference ◽  
Markov Jump Processes

Bayesian analysis for Markov jump processes (MJPs) is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding, thus its applicability is limited to a small class of problems. In this paper, we describe the application of Riemann manifold Markov chain Monte Carlo (MCMC) methods using an approximation to the likelihood of the MJP that is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient whereas the convergence rate and mixing of the chains allow for fast MCMC inference. The methodology is evaluated using numerical simulations on two problems from chemical kinetics and one from systems biology.

Sign in / Sign up

Export Citation Format

Share Document