{ "title": "An Estimating Parameter of the Mean in Normal Distribution by Maximum Likelihood, Bayes, and Markov Chain Monte Carlo Methods", "authors": "Autcha Araveeporn", "country": "Thailand", "institution": "King Mongkut's Institute of Technology Ladkrabang", "volume": "117", "journal": "International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering", "pagesStart": 441, "pagesEnd": 445, "ISSN": "1307-6892", "URL": "http:\/\/waset.org\/publications\/10005322", "abstract": "

This paper is to compare the parameter estimation of
\r\nthe mean in normal distribution by Maximum Likelihood (ML),
\r\nBayes, and Markov Chain Monte Carlo (MCMC) methods. The ML
\r\nestimator is estimated by the average of data, the Bayes method is
\r\nconsidered from the prior distribution to estimate Bayes estimator,
\r\nand MCMC estimator is approximated by Gibbs sampling from
\r\nposterior distribution. These methods are also to estimate a parameter
\r\nthen the hypothesis testing is used to check a robustness of the
\r\nestimators. Data are simulated from normal distribution with the true
\r\nparameter of mean 2, and variance 4, 9, and 16 when the sample
\r\nsizes is set as 10, 20, 30, and 50. From the results, it can be seen
\r\nthat the estimation of MLE, and MCMC are perceivably different
\r\nfrom the true parameter when the sample size is 10 and 20 with
\r\nvariance 16. Furthermore, the Bayes estimator is estimated from the
\r\nprior distribution when mean is 1, and variance is 12 which showed
\r\nthe significant difference in mean with variance 9 at the sample size
\r\n10 and 20.<\/p>\r\n", "references": null, "publisher": "World Academy of Science, Engineering and Technology", "index": "International Science Index 117, 2016" }