Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Bayesian analysis of directional conditionally autoregressive models

방향성 공간적 조건부 자기회귀 모형의 베이즈 분석 방법

  • Kyung, Minjung (Department of Statistics, Duksung Women's University)
  • 경민정 (덕성여자대학교 정보통계학과)
  • Received : 2016.06.17
  • Accepted : 2016.07.11
  • Published : 2016.09.30
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Abstract

Counts or averages over arbitrary regions are often analyzed using conditionally autoregressive (CAR) models. The spatial neighborhoods within CAR model are generally formed using only the inter-distance or boundaries between the sub-regions. Kyung and Ghosh (2009) proposed a new class of models to accommodate spatial variations that may depend on directions, using different weights given to neighbors in different directions. The proposed model, directional conditionally autoregressive (DCAR) model, generalized the usual CAR model by accounting for spatial anisotropy. Bayesian inference method is discussed based on efficient Markov chain Monte Carlo (MCMC) sampling of the posterior distributions of the parameters. The method is illustrated using a data set of median property prices across Greater Glasgow, Scotland, in 2008.

공간통계 방법 중 지역에 대한 어떤 집합체 자료나 평균자료들을 분석하는데 일반적으로 공간적 자기회귀 (conditionally autoregressive) 모형을 사용한다. 공간적 자기회귀 모형에 정의되는 공간적 이웃 소지역들은 중점의 거리나 근접성으로 정의된다. Kyung과 Ghosh (2009)는 방향에 따라서 이웃간 자기상관성의 크기가 다른 확장된 공간 모형을 제시하였다. 제안된 방향적 조건부 자기회귀 (directional conditionally autoregressive) 모형은 고유 이방성을 모형화하여 기존의 CAR과정을 일반화한다. 제시한 방향적 조건부 자기회귀모형의 모수추정으로 마르코프 체인 몬테 카를로 방법을 기반으로 한 베이즈 추정법을 제시한다. 제시한 모형을 스코틀랜드 그레이터 글래스고우의 로그변환된 부동산 가격에 적용하여 조건부 자기회귀모형과 비교하였다.

Keywords

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