• Journal of the Korean Statistical Society
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• v.27 no.4
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• pp.385-396
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• 1998

A computing method of fractional Bayes factor (FBF) for a point null hypothesis is explained. We propose alternative form of FBF that is the product of density ratio and a quantity using the generalized Savage-Dickey density ratio method. When it is difficult to compute the alternative form of FBF analytically, each term of the proposed form can be estimated by MCMC method. Finally, two examples are 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.

• The Korean Journal of Applied Statistics
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• v.11 no.1
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• pp.97-111
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• 1998

This paper suggests a Bayesian method for testing first-order markov correlation among linear regression disturbances. As a Bayesian test criterion, Bayes factor is derived in the form of generalized Savage-Dickey density ratio that is easily estimated by means of posterior simulation via Gibbs sampling scheme. Performance of the Bayesian test is evaluated and examined based upon a Monte Carlo experiment and an empirical data analysis. Efficiency of the posterior simulation is also examined.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.909-922
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• 2014

This paper reviews Bayesian inference with inequality constraints. It focuses on ⅰ) comparison of models with various inequality/equality constraints on parameters, ⅱ) multiple tests on equalities of parameters when parameters are under inequality constraints, ⅲ) multiple test on equalities of score parameters in models for contingency tables with ordinal categorical variables.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.141-150
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• 2000

In this paper we propose a method of computing Bayes factor to detect an outlier in a random effects model. When no information is available and hence improper noninformative priors should be used Bayes factor includes the unspecified constants and has complicated computational burden. To solve this problem we use the fractional Bayes factor (FBF) of O-Hagan(1995) and the generalized Savage0-Dickey density ratio of Verdinelli and Wasserman (1995) The proposed method is applied to outlier deterction problem We perform a simulation of the proposed approach with a simulated data set including an outlier and also analyze a real data set.

• Journal of Korean Society for Quality Management
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• v.24 no.4
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• pp.190-206
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• 1996

In case measurements are made on units of production in time order, it is reasonable to expect that the measurement errors will sometimes be first order autocorrelated, and a technique to test such autocorrelation is required to give good control of the productive process. Tool-wear process provide an example for which regression model can sometimes be useful in modeling and controlling the process. For the control of such process, we present a simple method for testing first order autocorrelation in regression errors. The method is based on Bayesian test method via Bayes factor and derived by observing that in general, a Bayes factor can be written as the product of a quantity called the Savage-Dickey density ratio and a correction factor ; both terms are easily estimated from Gibbs sampling technique. Performance of the method is examined by means of Monte Carlo simulation. It is noted that the test not only achieves satisfactory power but eliminates the inconvenience occurred in using the well-known Durbin-Watson test.