Volume 5, Issue 1, February 2019, Page: 1-5
An Estimation of Unknown Variance of a Normal Distribution: Application to Borno State Rainfall Data
Adegoke Taiwo Mobolaji, Department of Statistics, University of Ilorin, Ilorin, Nigeria
Nicholas Pindar Dibal, Department of Mathematical Sciences, University of Maiduguri, Maiduguri, Nigeria
Yahaya Abdullahi Musa, Department of Mathematical Sciences, University of Maiduguri, Maiduguri, Nigeria
Received: Dec. 26, 2018;       Accepted: Feb. 15, 2019;       Published: Mar. 28, 2019
DOI: 10.11648/j.ijdsa.20190501.11      View  67      Downloads  28
Abstract
The Bayesian estimation of unknown variance of a normal distribution is examined under different priors using Gibbs sampling approach with an assumption that mean is known. The posterior distributions for the unknown variance of the Normal distribution were derived using the following priors: Inverse Gamma distribution, Inverse Chi-square distribution and Levy distribution of the unknown variance of a normal distribution and Gumbel Type II. R functions are developed to study the various statistical simulation samples generated from Winbugs.
Keywords
Normal Distribution, Prior Distribution, Posterior Distribution, Bayesian Estimation, Inverse Gamma Distribution, Inverse Chi-Square Distribution, Levy Distribution, Gumbel Type II Distribution
To cite this article
Adegoke Taiwo Mobolaji, Nicholas Pindar Dibal, Yahaya Abdullahi Musa, An Estimation of Unknown Variance of a Normal Distribution: Application to Borno State Rainfall Data, International Journal of Data Science and Analysis. Vol. 5, No. 1, 2019, pp. 1-5. doi: 10.11648/j.ijdsa.20190501.11
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
Beaumont, M. A., Zhang, W. and Balding, D. J. (2002). Approximate Bayesian computation in population genetics. Genetics, 162, 2025-2035.
[2]
Cox, D. R. and Reid, N. (2004). A note on pseudo likelihood constructed from marginal densities. Biometrika, 91, 729-737.
[3]
Dean, T. A., Singh, S. S., Jasra A. and Peters G. W. (2011). Parameter estimation for hidden Markov models with intractable likelihoods. Arxiv preprint arXiv: 1103.5399v1.
[4]
Didelot, X., Everitt, R. G., Johansen, A. M. and Lawson, D. J. (2011). Likelihood-free estimation of model evidence. Bayesian Analysis, 6, 49-76.
[5]
Fearnhead, P. and Prangle, D. (2012). Constructing Summary Statistics for Approximate Bayesian Computation: Semi-automatic ABC (with discussion). Journal of the Royal Statistical Society.
[6]
Kelvin P. Murphy (2017). Conjugate Bayesian analysis of the Gaussian distribution. Handbook on Bayesian Statistics, 1-29.
[7]
Marin, J., Pudlo, P., Robert, C. P. and Ryder, R. (2011). Approximate Bayesian Computational methods. Statistics and Computing.
[8]
Obisesan, K. (2015). Change-point detection in time series with hydrological applications. Master’s thesis, University College London.
[9]
Perreault, L., Bernier, J., Bobee B., Parent, E. (2000), Bayesian change-point analysis in hydro meteorological time series. Part 1. The normal model revisited. Journal of Hydrology 235, 221–241.
[10]
Pritchard, J. K., Seielstad, M. T., Perez-Lezaun, A., and Feldman, M. T. (1999). Population Growth of Human Y Chromosomes: A Study of Y. Chromosome Microsatellites. Molecular Biology and Evolution 16: 1791 1798.
[11]
Rebecca C. Steorts, (2016). Baby Bayes using R.
[12]
Robert, C. P., Cornuet, J., Marin, J. and Pillai, N. S. (2011). Lack of confidence in ABC model choice. Proceedings of the National Academy of Sciences of the United States of America 108: 15112–15117.
[13]
Tendor Mihai Moldovan, (2010). The Conjugate Prior for the Normal Distribution, Technical report, 1-6.
[14]
Weisstein, E. W. (2012). Maximum Likelihood. From MathWorld—A Wolfram Web Resource. http://mathwor ld.wolfram.com/MaximumLikelihood.html.
[15]
Wilkinson, R. D. (2008). Approximate Bayesian computation (ABC) gives exact results under the assumption of error model. Arxiv preprint arXiv: 081 1.3355.
[16]
Yahya, W. B., Obisesan, K. O. and Adegoke, T. M. (2017), Bayesian Change-Point Modelling of Rainfall Distributions in Nigeria. Proceedings of 1ST International Annual Conference of Nigeria Statistical Society, held at University of Ibadan Conference Center, Ibadan, Nigeria, 3RD to 5TH of April, 2017, 1, 59-63.
Browse journals by subject