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On Bayesian estimation of regression models subject to uncertainty about functional constraints
김혜중,최태련 한국통계학회 2014 Journal of the Korean Statistical Society Vol.43 No.1
In this paper, we provide a Bayesian estimation procedure for the regression modelswhen the constraint of the regression function needs to be incorporated in modelingbut such a restriction is uncertain. For this purpose, we consider a family of rectanglescreened multivariate Gaussian prior distributions in order to reflect uncertainty about thefunctional constraint, and propose the Bayesian estimation procedure of the regressionmodels based on two stages of a prior hierarchy of the functional constraint, referredto as hierarchical screened Gaussian regression models (HSGRM). Specifically, we exploretheoretical properties of the proposed estimation procedure by deriving the posteriordistribution and predictive distribution of the unknown parameters under HSGRM inanalytic forms, and discuss specific applications to regression models with uncertainfunctional constraints that can be explained in the context of HSGRM.
Bayesian Robust Analysis for Non-Normal Data Based on a Perturbed-t Model
김혜중 한국통계학회 2006 Journal of the Korean Statistical Society Vol.35 No.4
The article develops a new class of distributions by introducing a non-negative perturbing function tot distribution having location and scaleparameters. The class is obtained by using transformations and condition-ing. The class strictly includest and skew-t distributions. It provides yetother models useful for selection modeling and robustness analysis. Analyticforms of the densities are obtained and distributional properties are studied.These developments are followed by an easy method for estimating the dis-tribution by using Markov chain Monte Carlo. It is shown that the methodis straightforward to specify distributionally and to implement computation-ally, with output readily adopted for constructing required criterion. Themethod is illustrated by using a simulation study.AMS 2000 subject classications.Primary 62H10; Secondary 62F15.Keywords.Perturbedt-distribution, non-normal data, Bayesian robust analysis.1. IntroductionSuppose that the model where a random variableZ is distributed with densityg(zj) and that it is desired to make inferences about;where is aq-dimensionalvector of unknown parameters. The usual statistical analysis assumes that a ran-dom sample Z1;:;Z n fromg(zj) can be observed. There are many situations,however, in which such a random sample might not be available, for instance, if itis too dicult or too costly to obtain. Then statistical models have to be devel-oped to incorporate the non-randomness or bias in the observations. Weighteddistributions (Rao, 1985) arise when the density of the potential observationz gets distorted so that it is multiplied by some non-negative weight functionReceived February 2006; accepted October 2006.yThis research was supported by the Korea Research Foundation Grant funded by the KoreanGovernment (MOEHRD) KRF-2005-041-C00089.
김혜중,김주성 한국통계학회 2005 Journal of the Korean Statistical Society Vol.34 No.3
The marginal distribution of X is considered when (X; Y ) has a truncated bivariate t-distribution. This paper mainly focuses on the marginal nontruncated distribution of X where Y is truncated below at its mean and its observations are not available. Several properties and applications of this distribution, including relationship with Azzalini’s skew-normal distribution, are obtained. To circumvent inferential problem arises from adopting the frequentist’s approach, a Bayesian method utilizing a data augmentation method is suggested. Illustrative examples demonstrate the performance of the method.
김혜중 한국통계학회 2010 Journal of the Korean Statistical Society Vol.39 No.1
A class of weighted elliptical models useful for analyzing nonnormal and bimodal multivariate data is introduced. It is obtained from the marginal distribution of a centrally truncated multivariate elliptical distribution. As a special case, a finite mixture of weighted multinormal distribution is examined in detail, establishing connections with the multinormal and the finite mixture of multinormal. The special class of distributions is studied from several aspects such as weighting of probability density functions, association with centrally truncated distributions, and a finite scale mixture scheme. The relationships among these aspects are given, and various properties of the class are also discussed. For the inference of the class, an MCMC procedure and its numerical example are provided.
스펙트럼분석 기반의 미기상해석모듈 평가알고리즘 제안 및 시계열 군집분석에의 응용
김혜중,곽화륜,김유나,최영진,Kim, Hea-Jung,Kwak, Hwa-Ryun,Kim, Yu-Na,Choi, Young-Jean 한국데이터정보과학회 2015 한국데이터정보과학회지 Vol.26 No.1
In meteorological field, many researchers have tried to develop micro scale weather analysis modules for providing real-time weather information service in the metropolitan area. This effort enables us to cope with various economic and social harms coming from serious change in the micro meteorology of a metropolitan area due to rapid urbanization such as quantitative expansions in its urban activity, growth of population, and building concentration. The accuracy of the micro scale weather analysis modules (MSWAM) directly related to usefulness and quality of the real-time weather information service in the metropolitan area. This paper design a evaluation system along with verification tools that sufficiently accommodate spatio-temporal characteristics of the outputs of the MSWAM. For this we proposes a test for the equality of mean vectors of the output series of the MSWAM and corresponding observed time series by using a spectral analysis technique. As a byproduct, a time series cluster analysis method, using a function of the test statistic as the distance measure, is developed. A real data application is given to demonstrate the utility of the method. 기상분야에서는 다양한 미기상해석모듈 (micro scale weather analysis module)을 개발하여 초고분해능의 기상정보서비스를 실시간으로 제공하고자 노력하고 있다. 이와 같은 연구들은 최근 대도시의 양적인 팽창으로 인해 발생되는 도시 미기상 (micro meteorology)의 급격한 변화에 효과적으로 대처할 수 있는 경제적 사회적 활동을 가능케 한다. 따라서 미기상해석모듈의 정확성은 도시 미기상정보서비스의 품질 및 효용성에 직결된다. 본 논문은 미기상해석모듈이 생성하는 시-공간적인 특성을 가진 양적인 결과물의 정확성에 대한 평가체계를 설계하였다. 이와 더불어 평가체계의 구성에 사용될 평가도구로써 시계열평균의 동일성검정 알고리즘을 스펙트럼 분석기법으로 구축하였으며, 동일성 검정통계의 함수를 거리측도로 사용하는 시계열 군집분석법도 함께 개발하였다. 또한, 사례연구를 통해 제안된 군집분석법과 평가알고리즘의 유용성을 보였다.
기상인자의 주기성 분석 및 일반화 선형모형을 이용한 강수영향분석: 2004KEOP의 한반도 남서지방 8개 지역 기상관측자료사용
김혜중,염준근,이영섭,김영아,정효상,조천호,Kim Hea-Jung,Yum Joonkeun,Lee Yung-Seop,Kim Young-Ah,Chung Hyo-Sang,Cho Chun-Ho 한국통계학회 2005 응용통계연구 Vol.18 No.2
본 연구에서는 2004년 기상청 집중관측기간(KEOP)에 수집된 지상관측자료를 사용하여 한반도 남서지방의 지역별(해남 외 7개 지역) 기상인자들의 주기성과 이들이 강수현상에 미치는 영향을 분석하였다. 이를 위하여 기술통계와 스펙트럴분석을 사용하여 주기성을 분석하고, 관측기간 및 지역별 랜덤효과를 반영할 수 있는 일반화 선형모형을 제시하여 강수현상에 미치는 기상인자들의 영향을 분석했다. 분석결과에 의하면 기상인자들과 강수현상은 연관성을 가지며 특정주기에 따라 변동하는 것으로 나타났으며, 기상인자들은 지역에 따라 상이한 패턴으로 강수현상에 영향을 미치는 것으로 나타났다. This article summarizes our research on estimation of area-specific and time-adjusted rainfall rates during 2004KEOP (Korea enhanced observation period: June 1, $2004{\sim}$ August 31, 2004). The rainfall rate is defined as the proportion of rainfall days per week and areas are consisting of Haenam, Yeosu, Janghung, Heuksando, Gwangju, Mokpo, Jindo, and Wando. Our objectives are to analyze periodicity in area-specific precipitation and the meteorological measures and investigate the relationships between the geographic pattern of the rainfall rates and the corresponding pattern in potential explanatory covariates such as temperature, wind, wind direction, pressure, and humidity. A generalized linear model is introduced to implement the objectives and the patterns are estimated by considering a set of rainfall rates produced using samples from the posterior distribution of the population rainfall rates.