Noninformative priors for common scale parameter in the regular Pareto distributions

Abstract

In this paper, we introduce the noninformative priors such as the matching priors and the reference priors for the common scale parameter in the Pareto distributions. It turns out that the posterior distribution under the reference priors is not proper, and Jeffreys' prior is not a matching prior. It is shown that the proposed first order prior matches the target coverage probabilities in a frequentist sense through simulation study.

Noninformative Priors for the Ratio of the Scale Parameters in the Inverted Exponential Distributions

“…Quite often reference priors satisfy the matching criterion described earlier. This approach is very successful in various practical problems (Kang, 2011;Kang et al, 2012).…”

Noninformative priors for the scale parameter in the generalized Pareto distribution

“…Ghosh and Mukerjee (1992) and Bernardo (1989,1992) gave 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, 2011;Kang et al, 2012Kang et al, , 2013. Quite often reference priors satisfy the matching criterion described earlier.…”

Noninformative priors for the log-logistic distribution

“…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, 2011;Kim et al 2009). Quite often reference priors satisfy the matching criterion described earlier.…”