Bayesian inference on M/M/1 queue under asymmetric loss function using Markov Chain Monte Carlo method

2021 ◽  
pp. 1-21
Author(s):  
V. Deepthi ◽  
Joby K. Jose
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Inference ◽  
Monte Carlo Method ◽  
Loss Function ◽  
Asymmetric Loss ◽  
Asymmetric Loss Function

Bayesian Estimation of an M/M/𝑅 Queue with Heterogeneous Servers Using Markov Chain Monte Carlo Method

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
V. Deepthi ◽  
Joby K. Jose
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Method ◽  
Loss Function ◽  
Prior Distribution ◽  
Arrival Rate ◽  
Heterogeneous Servers ◽  
Squared Error Loss Function ◽  
Service Rates

AbstractIn this paper, we consider the Bayesian inference of M/M/𝑅 queue with 𝑅 heterogeneous servers with service rates \mu_{1},\mu_{2},\ldots,\mu_{R}, where \mu_{1}>\mu_{2}>\cdots>\mu_{R}. Assuming multivariate gamma prior distribution for service rates and gamma prior distribution for arrival rate 𝜆, we derive the conditional posterior densities of mean arrival rate and mean service rates. We apply the Markov chain Monte Carlo method and compute the Bayes estimates and credible interval for the M/M/3 queue, as a particular case of the M/M/𝑅 queue under squared error loss function, entropy loss function and linex loss function corresponding to a different set of hyperparameters.

scholarly journals Bayesian inference for multistage and other incomplete designs

2020 ◽  
Author(s):  
Jesse Koops ◽  
Timo Bechger ◽  
Gunter Maris
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Inference ◽  
Monte Carlo Method ◽  
Simulated Data ◽  
Operating Characteristics ◽  
Multistage Testing ◽  
Incomplete Designs ◽  
San Martín

Following Maris, Bechger and San-Martin (2015), we develop a Markov chain - Monte Carlo method for Bayesian inference tailored to handle data collected in multistage and other incomplete designs. We illustrate its operating characteristics with simulated data, and provide a real application. To appear as: Koops, J. and Bechger, T. and Maris, G. (2021); Bayesian inference for multistage and other incomplete designs. In Research for Practical Issues and Solutions in Computerized Multistage Testing. Routledge, London.

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