Noninformative priors for the log-logistic distribution

Abstract

In this paper, we develop the noninformative priors for the scale parameter and the shape parameter in the log-logistic distribution. We developed the first and second order matching priors. It turns out that the second order matching prior matches the alternative coverage probabilities, and is a highest posterior density matching prior. Also we revealed that the derived reference prior is the second order matching prior for both parameters, but Jeffrey's prior is not a second order matching prior. We showed that the proposed reference prior matches the target coverage probabilities in a frequentist sense through simulation study, and an example based on real data is given.

Default Bayesian testing for scale parameters in the log-logistic distributions

“…by Kang et al (2014a). Then from the likelihood (3.2) and the reference prior (3.3), the element m b 1 (x, y) of the FBF under H 1 is given by…”

“…So under minimal training sample, we only calculate the marginal densities for the hypotheses H 1 and H 2 , respectively. The marginal densities of (X j1 , X j2 , Y k1 , Y k2 ) are finite for all 1 ≤ j 1 < j 2 ≤ n and 1 ≤ k 1 < k 2 ≤ m under each hypothesis (see Theorem 3.1 of Kang et al (2014a)). Thus we conclude that any training sample of size 4 is a minimal training sample.…”

Noninformative priors for product of exponential means

“…Ghosh and Mukerjee (1992), and Bernardo (1989, 1992) give a general algorithm to derive a reference prior by splitting the parameters into several groups according to their order of inferential importance. This approach is very successful in various practical problems (Kang et al, 2013(Kang et al, , 2014. Quite often reference priors satisfy the matching criterion described earlier.…”

Noninformative priors for linear combinations of exponential means

“…Ghosh and Mukerjee (1992), and Bernardo (1989,1992) give a general algorithm to derive a reference prior by splitting the parameters into several groups according to their order of inferential importance. This approach is very successful in various practical problems (Kang, 2013;Kang et al 2013Kang et al , 2014. Quite often reference priors satisfy the matching criterion described earlier.…”