The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Posterior density estimation of Kappa via Gibbs sampler in the beta-binomial model

베타-이항 분포에서 Gibbs sampler를 이용한 평가 일치도의 사후 분포 추정

  • 엄종석 ((136-042) 서울시 성북구 삼선동 2가 한성대학교 전산통계학과) ;
  • 최일수 ((120-749) 서울시 서대문구 신촌동 연세대학교 응용통계학과) ;
  • 안윤기 ((120-749) 서울시 서대문구 신촌동 연세대학교 응용통계학과)
  • Published : 1994.09.01
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Abstract

Beta-binomial model, which is reparametrized in terms of the mean probability $\mu$ of a positive deagnosis and the $\kappa$ of agreement, is widely used in psychology. When $\mu$ is close to 0, inference about $\kappa$ become difficult because likelihood function becomes constant. We consider Bayesian approach in this case. To apply Bayesian analysis, Gibbs sampler is used to overcome difficulties in integration. Marginal posterior density functions are estimated and Bayesian estimates are derived by using Gibbs sampler and compare the results with the one obtained by using numerical integration.

평가자간 평가 일치도(measure of agreement)를 나타내는 모수 $\kappa$와 양성 반응 비율 $\mu$를 지닌 베타-이항 분포 모형은 심리학 분야에서 많이 다루어지는 모형이다. 이 모형에서 $\kappa$에 대한 추정은 $\mu$가 0에 가까운 값을 가질 때 우도함수를 이용한 전통적 추론 방법의 적용이 어렵다. 본 논문에서는 이러한 문제를 Gibbs sampler를 이용한 Bayesian 분석 방법을 적용시켜 주변 사후 밀도 함수를 추정하였으며 이를 이용하여 Bayesian 추정값도 구하였다.

Keywords

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