Noninformative priors for the scale parameter in the generalized Pareto distribution

Kang, Sang Gil

doi:10.7465/jkdi.2013.24.6.1521

Cited by 5 publications

(5 citation statements)

References 32 publications

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“…For prior specifications, we use non‐informative priors for both models. In particular, we use Jeffreys priors [see Kang () for details]. Thus, under model M 0 , the prior for ( α 0 , β 0 ) is

π_{0} (() α_{0}, β_{0}) \propto β_{0}^{prefix- 1} {(1 + α_{0})}^{prefix- 1} {(1 + 2 α_{0})}^{prefix- 1 true/ 2} .

Under model M 3 , assuming independent a priori , the joint prior for ( α 1 , α 2 , β 1 , β 2 ) is

\begin{matrix} π_{3} (α_{1}, α_{2}, β_{1}, β_{2}) \propto β_{1}^{- 1} {((), 1 + α_{1})}^{- 1} \\ \times {((), 1 + 2 α_{1})}^{- 1 / 2} β_{2}^{- 1} {((), 1 + α_{2})}^{- 1} {((), 1 + 2 α_{2})}^{- 1 / 2} . \end{matrix}

Finally, we impose a discrete uniform prior on τ , which has been conventionally used in the literature of CP analysis (Yang, ).…”

Section: Bayesian Cp Modelsmentioning

confidence: 99%

Bayesian change point analysis for extreme daily precipitation

Chen

Kim

et al. 2016

Intl Journal of Climatology

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Change point (CP) analysis of extreme precipitation plays a key role to incorporate non‐stationarity in flood predictions under climate change. This article provides a Bayesian method to detect the CP frequently appearing in extreme precipitation data. Unlike most published work based on a normal distribution, we allow for the model to follow a generalized Pareto distribution to fit extreme precipitation over a high threshold with a CP, which can effectively utilize tail behaviour of the distribution. The Bayesian CP detection is investigated on four models: a no change model, a shape change model, a scale change model, and both a shape and scale change model. Model selection is performed using the Bayes factor and model posterior probability; the posterior means of the unknown CP and the model parameters before and after the CP can be obtained based on the selected CP model. Simulation studies and a real data example are provided to demonstrate the proposed methodologies. Finally, model uncertainty issues in the frequency analysis are extensively discussed. It is found that considering the abrupt and sustained CP in extreme precipitation is important when performing hydraulic or hydrologic design.

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π_{0} (() α_{0}, β_{0}) \propto β_{0}^{prefix- 1} {(1 + α_{0})}^{prefix- 1} {(1 + 2 α_{0})}^{prefix- 1 true/ 2} .

Under model M 3 , assuming independent a priori , the joint prior for ( α 1 , α 2 , β 1 , β 2 ) is

\begin{matrix} π_{3} (α_{1}, α_{2}, β_{1}, β_{2}) \propto β_{1}^{- 1} {((), 1 + α_{1})}^{- 1} \\ \times {((), 1 + 2 α_{1})}^{- 1 / 2} β_{2}^{- 1} {((), 1 + α_{2})}^{- 1} {((), 1 + 2 α_{2})}^{- 1 / 2} . \end{matrix}

Finally, we impose a discrete uniform prior on τ , which has been conventionally used in the literature of CP analysis (Yang, ).…”

Section: Bayesian Cp Modelsmentioning

confidence: 99%

Bayesian change point analysis for extreme daily precipitation

Chen

Kim

et al. 2016

Intl Journal of Climatology

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“…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.…”

Section: Introductionmentioning

confidence: 98%

Noninformative priors for linear combinations of exponential means

Lee¹,

Kim²,

Kang

2016

Journal of the Korean Data and Information Science Society

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In this paper, we develop the noninformative priors for the linear combinations of means in the exponential distributions. We develop the matching priors and the reference priors. The matching priors, the reference prior and Jeffreys' prior for the linear combinations of means are developed. It turns out that the reference prior and Jeffreys' prior are not a matching prior. We show that the proposed matching prior matches the target coverage probabilities much more accurately than the reference prior and Jeffreys' prior in a frequentist sense through simulation study, and an example based on real data is given.

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“…In a Bayesian point of view, many authors have studied statistical inferences on Pareto distribution (e.g., Press, 1983, 1989;Geisser, 1984Geisser, , 1985Lwin, 1972;Nigm and Hamdy, 1987;Tiwari, Yang and Zalkikar, 1996;Ko and Kim, 1999;Fernández, 2008;Kim et al, 2009;Kang, 2010).…”

Section: Introductionmentioning

confidence: 99%

“…Although the family was originally applied to analyze socio-economic and natural phenomena with long tail, the family has potential for modeling reliability and lifetime data as well (Arnold and Press, 1983). The Pareto distribution has been used by many authors in a Bayesian viewpoint (e.g., Press, 1983, 1989;Geisser, 1984Geisser, , 1985Lwin, 1972;Nigm and Hamdy, 1987;Tiwari et al, 1996;Ko and Kim, 1999;Fernández, 2008;Kim et al, 2009;Kang, 2010). For the common scale parameter, Elfessi and Jin (1996) derived a class of improved estimators which uniformly dominates the MLE under a class of convex scale invariant loss functions.…”

Section: Introductionmentioning

confidence: 99%

Noninformative priors for common scale parameter in the regular Pareto distributions

Kang¹,

Kim²,

Kim

2012

Journal of the Korean Data and Information Science Society

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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.

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Noninformative priors for the scale parameter in the generalized Pareto distribution

Cited by 5 publications

References 32 publications

Bayesian change point analysis for extreme daily precipitation

Bayesian change point analysis for extreme daily precipitation

Noninformative priors for linear combinations of exponential means

Noninformative priors for common scale parameter in the regular Pareto distributions

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