• Title/Summary/Keyword: collapsed Gibbs sampler

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A nonparametric Bayesian seemingly unrelated regression model (비모수 베이지안 겉보기 무관 회귀모형)

  • Jo, Seongil;Seok, Inhae;Choi, Taeryon
    • The Korean Journal of Applied Statistics
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    • v.29 no.4
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    • pp.627-641
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    • 2016
  • In this paper, we consider a seemingly unrelated regression (SUR) model and propose a nonparametric Bayesian approach to SUR with a Dirichlet process mixture of normals for modeling an unknown error distribution. Posterior distributions are derived based on the proposed model, and the posterior inference is performed via Markov chain Monte Carlo methods based on the collapsed Gibbs sampler of a Dirichlet process mixture model. We present a simulation study to assess the performance of the model. We also apply the model to precipitation data over South Korea.

Efficient Bayesian Inference on Asymmetric Jump-Diffusion Models (비대칭적 점프확산 모형의 효율적인 베이지안 추론)

  • Park, Taeyoung;Lee, Youngeun
    • The Korean Journal of Applied Statistics
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    • v.27 no.6
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    • pp.959-973
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    • 2014
  • Asset pricing models that account for asymmetric volatility in asset prices have been recently proposed. This article presents an efficient Bayesian method to analyze asset-pricing models. The method is developed by devising a partially collapsed Gibbs sampler that capitalizes on the functional incompatibility of conditional distributions without complicating the updates of model components. The proposed method is illustrated using simulated data and applied to daily S&P 500 data observed from September 1980 to August 2014.

Grid-based Gaussian process models for longitudinal genetic data

  • Chung, Wonil
    • Communications for Statistical Applications and Methods
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    • v.29 no.1
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    • pp.65-83
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    • 2022
  • Although various statistical methods have been developed to map time-dependent genetic factors, most identified genetic variants can explain only a small portion of the estimated genetic variation in longitudinal traits. Gene-gene and gene-time/environment interactions are known to be important putative sources of the missing heritability. However, mapping epistatic gene-gene interactions is extremely difficult due to the very large parameter spaces for models containing such interactions. In this paper, we develop a Gaussian process (GP) based nonparametric Bayesian variable selection method for longitudinal data. It maps multiple genetic markers without restricting to pairwise interactions. Rather than modeling each main and interaction term explicitly, the GP model measures the importance of each marker, regardless of whether it is mostly due to a main effect or some interaction effect(s), via an unspecified function. To improve the flexibility of the GP model, we propose a novel grid-based method for the within-subject dependence structure. The proposed method can accurately approximate complex covariance structures. The dimension of the covariance matrix depends only on the number of fixed grid points although each subject may have different numbers of measurements at different time points. The deviance information criterion (DIC) and the Bayesian predictive information criterion (BPIC) are proposed for selecting an optimal number of grid points. To efficiently draw posterior samples, we combine a hybrid Monte Carlo method with a partially collapsed Gibbs (PCG) sampler. We apply the proposed GP model to a mouse dataset on age-related body weight.

Bayesian inference on multivariate asymmetric jump-diffusion models (다변량 비대칭 라플라스 점프확산 모형의 베이지안 추론)

  • Lee, Youngeun;Park, Taeyoung
    • The Korean Journal of Applied Statistics
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    • v.29 no.1
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    • pp.99-112
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    • 2016
  • Asymmetric jump-diffusion models are effectively used to model the dynamic behavior of asset prices with abrupt asymmetric upward and downward changes. However, the estimation of their extension to the multivariate asymmetric jump-diffusion model has been hampered by the analytically intractable likelihood function. This article confronts the problem using a data augmentation method and proposes a new Bayesian method for a multivariate asymmetric Laplace jump-diffusion model. Unlike the previous models, the proposed model is rich enough to incorporate all possible correlated jumps as well as mention individual and common jumps. The proposed model and methodology are illustrated with a simulation study and applied to daily returns for the KOSPI, S&P500, and Nikkei225 indices data from January 2005 to September 2015.