• Journal of the Korean Data and Information Science Society
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• v.23 no.6
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• pp.1299-1308
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• 2012

This article deals with the problem of testing the equality of the scale parameters in nonregular Pareto distributions.We propose Bayesian hypothesis testing procedures for the equality of the scale parameters under the noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be de ned up to a multiplicative constant. So we propose the default Bayesia hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and a real data example are provided.

• Journal of the Korean Data and Information Science Society
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• v.25 no.2
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• pp.465-472
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• 2014

This article deals with the problem of testing the equality of the scale parameters in the half logistic distributions. We propose Bayesian hypothesis testing procedures for the equality of the scale parameters under the noninformative priors. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be dened up to a multiplicative constant. Thus we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.949-957
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• 2013

In this paper, we consider the problem of testing the equality of the scale parameters in two parameter exponential distributions. We propose Bayesian testing procedures for the equality of the scale parameters under the noninformative priors. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. Thus, we propose the default Bayesian testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

• Journal of the Korean Data and Information Science Society
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• v.23 no.3
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• pp.605-616
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• 2012

This article deals with the problem of testing on the common mean of several normal populations. We propose Bayesian hypothesis testing procedures for the common normal mean under the noninformative prior. The noninformative prior is usually improper and yields a calibration problem that makes the Bayes factor to be defined u to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1569-1579
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• 2014

This article deals with the problem of testing for the equality of the shape parameters in two inverse Weibull distributions. We propose Bayesian hypothesis testing procedures for the equality of the shape parameters under the noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

• Journal of the Korean Data and Information Science Society
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• v.27 no.3
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• pp.835-844
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• 2016

We develop the testing procedures about the homogeneity of the shape parameters of several inverse Gaussian distributions in our paper. We propose default Bayesian testing procedures for the shape parameters under the reference priors. The Bayes factor based on the proper priors gives the successful results for Bayesian hypothesis testing. For the case of the lack of information, the noninformative priors such as Jereys' prior or the reference prior can be used. Jereys' prior or the reference prior involves the undefined constants in the computation of the Bayes factors. Therefore under the reference priors, we develop the Bayesian testing procedures with the intrinsic Bayes factors and the fractional Bayes factor. Simulation study for the performance of the developed testing procedures is given, and an example for illustration is given.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1265-1273
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• 2011

This article deals with the problem of testing the equality of the location parameters in the half-normal distributions. We propose Bayesian hypothesis testing procedures for the equality of the location parameters under the noninformative prior. The non-informative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to arbitrary constants. This problem can be deal with the use of the fractional Bayes factor or intrinsic Bayes factor. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

• Journal of the Korean Statistical Society
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• v.28 no.1
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• pp.73-92
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• 1999

In Bayesian model selection or testing problems, one cannot utilize standard or default noninformative priors, since these priors are typically improper and are defined only up to arbitrary constants. The resulting Bayes factors are not well defined. A recently proposed model selection criterion, the intrinsic Bayes factor overcomes such problems by using a part of the sample as a training sample to get a proper posterior and then use the posterior as the prior for the remaining observations to compute the Bayes factor. Surprisingly, such Bayes factor can also be computed directly from the full sample by some proper priors, namely intrinsic priors. The present paper explains how to derive intrinsic priors for simple tree ordered exponential means. Some numerical results are also provided to support theoretical results and compare with classical methods.

• Journal of the Korean Data and Information Science Society
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• v.28 no.1
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• pp.217-225
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• 2017

This article deals with the problem of multiple hypothesis testing for the shape parameter in the generalized exponential distribution. We propose Bayesian hypothesis testing procedures for multiple hypotheses of the shape parameter with the noninformative prior. The Bayes factor with the noninformative prior is not well defined. The reason is that the most of the noninformative prior can be improper. Therefore we study the default Bayesian multiple hypothesis testing methods using the fractional and intrinsic Bayes factors with the reference priors. Simulation study is performed and an example is given.

• Communications for Statistical Applications and Methods
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• v.26 no.2
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• pp.217-238
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• 2019

With the advent of so-called "default" Bayesian hypothesis tests, scientists in applied fields have gained access to a powerful and principled method for testing hypotheses. However, such default tests usually come with a compromise, requiring the analyst to accept a one-size-fits-all approach to hypothesis testing. Further, such tests may not have the flexibility to test problems the scientist really cares about. In this tutorial, I demonstrate a flexible approach to generalizing one specific default test (the JZS t-test) (Rouder et al., Psychonomic Bulletin & Review, 16, 225-237, 2009) that is becoming increasingly popular in the social and behavioral sciences. The approach uses two results, the Savage-Dickey density ratio (Dickey and Lientz, 1980) and the technique of encompassing priors (Klugkist et al., Statistica Neerlandica, 59, 57-69, 2005) in combination with MCMC sampling via an easy-to-use probabilistic modeling package for R called Greta. Through a comprehensive mathematical description of the techniques as well as illustrative examples, the reader is presented with a general, flexible workflow that can be extended to solve problems relevant to his or her own work.