Noninformative priors for the nested design |
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| Institution: | 1. Department of Statistics, Kyungpook National University, Daegu 702-701, Republic of Korea;2. Department of Applied Statistics, Sangji University, Wonju 220-702, Republic of Korea;3. Department of Asset Managemental Science, Daegu Haany University, Kyungsan 712-240, Republic of Korea;1. Department of Biostatistics, University of Pittsburgh, 130 DeSoto Street, Pittsburgh, PA 15261, USA;2. Department of Mathematics and Applied Statistics, Sejong University, Republic of Korea;1. Department of Statistics, University of Florida, Gainesville, Florida, USA;2. Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, USA;3. Department of Statistics, Kyungpook National University, Daegu, South Korea;1. Department of Computer Science and Statistics, Chosum University, Gwangju 501-759, South Korea;2. Department of Mathematics, Hanyang University, 133-791 Seoul, South Korea;3. Indian Institute of Management, Post Box No. 16757, Calcutta 700 027, India;1. Dipartimento di Statistica, Probabilita’ e Statistiche Applicate, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, 00185 Roma, Italy;2. Università di Roma Tre, 00146 Roma, Italy;3. Università di Teramo, 64100 Teramo, Italy |
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| Abstract: | This paper considers noninformative priors for three-stage nested designs. It turns out that the noninformative prior given by Li and Stern (1997) is the one-at-a-time reference prior satisfying a second-order matching criterion when either the variance ratio or linear combinations of the means is of interest. Moreover, it is a joint probability matching prior when both the variance ratio and linear combinations of the means are of interest. These priors are compared with Jeffreys' prior in light of how accurately the coverage probabilities of Bayesian credible intervals match the corresponding frequentist coverage probabilities. |
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