TY - JOUR
T1 - A matching prior for the product of normal means based on the modified profile likelihood
AU - Kim, Yongku
AU - Lee, Woo Dong
AU - Kang, Sang Gil
N1 - Publisher Copyright:
© 2017, © 2017 Taylor & Francis Group, LLC.
PY - 2019/5/28
Y1 - 2019/5/28
N2 - In this paper, we develop a matching prior for the product of means in several normal distributions with unrestricted means and unknown variances. For this problem, properly assigning priors for the product of normal means has been issued because of the presence of nuisance parameters. Matching priors, which are priors matching the posterior probabilities of certain regions with their frequentist coverage probabilities, are commonly used but difficult to derive in this problem. We developed the first order probability matching priors for this problem; however, the developed matching priors are unproper. Thus, we apply an alternative method and derive a matching prior based on a modification of the profile likelihood. Simulation studies show that the derived matching prior performs better than the uniform prior and Jeffreys’ prior in meeting the target coverage probabilities, and meets well the target coverage probabilities even for the small sample sizes. In addition, to evaluate the validity of the proposed matching prior, Bayesian credible interval for the product of normal means using the matching prior is compared to Bayesian credible intervals using the uniform prior and Jeffrey’s prior, and the confidence interval using the method of Yfantis and Flatman.
AB - In this paper, we develop a matching prior for the product of means in several normal distributions with unrestricted means and unknown variances. For this problem, properly assigning priors for the product of normal means has been issued because of the presence of nuisance parameters. Matching priors, which are priors matching the posterior probabilities of certain regions with their frequentist coverage probabilities, are commonly used but difficult to derive in this problem. We developed the first order probability matching priors for this problem; however, the developed matching priors are unproper. Thus, we apply an alternative method and derive a matching prior based on a modification of the profile likelihood. Simulation studies show that the derived matching prior performs better than the uniform prior and Jeffreys’ prior in meeting the target coverage probabilities, and meets well the target coverage probabilities even for the small sample sizes. In addition, to evaluate the validity of the proposed matching prior, Bayesian credible interval for the product of normal means using the matching prior is compared to Bayesian credible intervals using the uniform prior and Jeffrey’s prior, and the confidence interval using the method of Yfantis and Flatman.
KW - Matching prior
KW - Modified profile likelihood
KW - Product of normal means
UR - http://www.scopus.com/inward/record.url?scp=85038110389&partnerID=8YFLogxK
U2 - 10.1080/03610918.2017.1410712
DO - 10.1080/03610918.2017.1410712
M3 - Article
AN - SCOPUS:85038110389
SN - 0361-0918
VL - 48
SP - 1312
EP - 1329
JO - Communications in Statistics Part B: Simulation and Computation
JF - Communications in Statistics Part B: Simulation and Computation
IS - 5
ER -