논문

The bspcov R package provides a Bayesian inference for covariance matrices. The bspcov is developed to aid in research that involves estimating constrained covariance matrices by enabling the use of state-of-the-art Bayesian inference methods. It consists of the main functions bmspcov, sbmspcov, bandPPP and thresPPP that conduct posterior inference for sparse or banded covariance matrices. The functions bmspcov and sbmspcov implement block Gibbs samplers based on beta-mixture and screened beta-mixture shrinkage priors, respectively. The functions bandPPP and thresPPP implement a direct posterior sampling from the post-processed posterior for banded and sparse covariance matrices. We demonstrate how to use the main functions with real data applications.

K Lee, K Lee, S Jo, K Lee · SoftwareX · 2025

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Eigenstructure Inference for High-Dimensional Covariance with Generalized Shrinkage Inverse-Wishart Page 1 Eigenstructure Inference for High-Dimensional Covariance with Generalized Shrinkage Inverse-Wishart Jaeyong Lee Department of Statistics Seoul National University June 11th 2025 Jointly with Seongmin Kim (Seoul National University, South Korea) Kwangmin Lee (Chonnam National University, South Korea) Sewon Park (Samsung SDS, South Korea) Page 2 Content Difficulties in the Inference of High-Dimensional Covariances Normal model with spiked covariance Inverse-Wishart prior Generalized Shrinkage Inverse-Wishart prior Theoretical Results for the posterior with gSIW prior Simulation Studies Page 3 Content Difficulties in the Inference of High-Dimensional Covariances Normal model with spiked covariance Inverse-Wishart prior Generalized Shrinkage Inverse-Wishart prior Theoretical …

J Lee · 학술지 미등록 · 2025

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In this paper, we study the conditional Dirichlet process (cDP) when a functional of a random distribution is specified. Specifically, we apply the cDP to the functional condition model, a nonparametric model in which a finite-dimensional parameter of interest is defined as the solution to a functional equation of the distribution. We derive both the posterior distribution of the parameter of interest and the posterior distribution of the underlying distribution itself. We establish two general limiting theorems for the posterior: one as the total mass of the Dirichlet process parameter tends to zero, and another as the sample size tends to infinity. We consider two specific models, the quantile model and the moment model, and propose algorithms for posterior computation, accompanied by illustrative data analysis examples. As a byproduct, we show that the Jeffreys substitute likelihood emerges as the limit of the marginal posterior in the functional condition model with a cDP prior, thereby providing a theoretical justification that has so far been lacking.

J Lee, K Lee, J Lee, S Jo · arXiv preprint arXiv:2506.15932 · 2025

인용 2회

In multivariate statistics, estimating the covariance matrix is essential for understanding the interdependence among variables. In high-dimensional settings, where the number of covariates increases with the sample size, it is well known that the eigenstructure of the sample covariance matrix is inconsistent. The inverse-Wishart prior, a standard choice for covariance estimation in Bayesian inference, also suffers from posterior inconsistency. To address the issue of eigenvalue dispersion in high-dimensional settings, the shrinkage inverse-Wishart (SIW) prior has recently been proposed. Despite its conceptual appeal and empirical success, the asymptotic justification for the SIW prior has remained limited. In this paper, we propose a generalized shrinkage inverse-Wishart (gSIW) prior for high-dimensional covariance modeling. By extending the SIW framework, the gSIW prior accommodates a broader class of prior distributions and facilitates the derivation of theoretical properties under specific parameter choices. In particular, under the spiked covariance assumption, we establish the asymptotic behavior of the posterior distribution for both eigenvalues and eigenvectors by directly evaluating the posterior expectations for two sets of parameter choices. This direct evaluation provides insights into the large-sample behavior of the posterior that cannot be obtained through general posterior asymptotic theorems. Finally, simulation studies illustrate that the proposed prior provides accurate estimation of the eigenstructure, particularly for spiked eigenvalues, achieving narrower credible intervals and higher coverage probabilities compared to existing …

S Kim, K Lee, S Park, J Lee · arXiv preprint arXiv:2505.20668 · 2025

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We study Bayesian inference in the spiked covariance model, where a small number of spiked eigenvalues dominate the spectrum. Our goal is to infer the spiked eigenvalues, their corresponding eigenvectors, and the number of spikes, providing a Bayesian solution to principal component analysis with uncertainty quantification. We place an inverse-Wishart prior on the covariance matrix to derive posterior distributions for the spiked eigenvalues and eigenvectors. Although posterior sampling is computationally efficient due to conjugacy, a bias may exist in the posterior eigenvalue estimates under high-dimensional settings. To address this, we propose two bias correction strategies: (i) a hyperparameter adjustment method, and (ii) a post-hoc multiplicative correction. For inferring the number of spikes, we develop a BIC-type approximation to the marginal likelihood and prove posterior consistency in the high-dimensional regime $p>n$. Furthermore, we establish concentration inequalities and posterior contraction rates for the leading eigenstructure, demonstrating minimax optimality for the spiked eigenvector in the single-spike case. Simulation studies and a real data application show that our method performs better than existing approaches in providing accurate quantification of uncertainty for both eigenstructure estimation and estimation of the number of spikes.

K Lee, S Park, S Kim, J Lee · arXiv preprint arXiv:2412.10753 · 2024

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In this paper, we estimate the seroprevalence against COVID-19 by country and derive the seroprevalence over the world. To estimate seroprevalence among adults, we use serological surveys (also called the serosurveys) conducted within each country. When the serosurveys are incorporated to estimate world seroprevalence, there are two issues. First, there are countries in which a serological survey has not been conducted. Second, the sample collection dates differ from country to country. We attempt to tackle these problems using the vaccination data, confirmed cases data, and national statistics. We construct Bayesian models to estimate the numbers of people who have antibodies produced by infection or vaccination separately. For the number of people with antibodies due to infection, we develop a hierarchical model for combining the information included in both confirmed cases data and national statistics. At …

K Lee, S Kim, S Jo, J Lee · Journal of Applied Statistics · 2024

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The response envelope model proposed by Cook et al. is an efficient method to estimate the regression coefficient under the context of the multivariate linear regression model. It improves estimation efficiency by identifying material and immaterial parts of responses and removing the immaterial variation. The response envelope model has been investigated only for continuous response variables. In this paper, we propose the multivariate probit model with latent envelope, in short, the probit envelope model, as a response envelope model for multivariate binary response variables. The probit envelope model takes into account relations between Gaussian latent variables of the multivariate probit model by using the idea of the response envelope model. We address the identifiability of the probit envelope model by employing the essential identifiability concept and suggest a Bayesian method for the parameter …

K Lee, Y Park · Biometrics · 2024

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K Lee, S Park, S Kim, J Lee · arXiv preprint arXiv:2412.10753 · 2024

인용 2회

We consider Bayesian inference of sparse covariance matrices and propose a post-processed posterior. This method consists of two steps. In the first step, posterior samples are obtained from the conjugate inverse-Wishart posterior without considering the sparse structural assumption. The posterior samples are transformed in the second step to satisfy the sparse structural assumption through a generalized thresholding function. This non-traditional Bayesian procedure is justified by showing that the post-processed posterior attains the optimal minimax rates under the spectral norm loss in high-dimensional settings. We also propose the post-processed posterior for contaminated data and apply it to the estimation of the sparse idiosyncratic covariance of the approximate factor model. The advantages of our method are demonstrated via a simulation study and a real data analysis with S&P 500 data.

K Lee, J Lee · Journal of Econometrics · 2023

인용 6회

We show the result of minimax convergence rate for bandable covariance case and more simulation results. We also give an example of application to Linear Discriminant Analysis. The proofs of lemmas and theorems in the main paper are represented. We provide the R code of the post-processed posterior procedure in the Github repository https://github.com/KwangminLee564/bandPPP.

K Lee, K Lee, J Lee · Bayesian Analysis · 2023

인용 13회

In the supplementary material, we give the minimax analysis for bandable covariance case in Section S1, and we consider the adaptation of the post-processed posterior with a prior on bandwidth k in Section S2. We also provide additional simulation study and real data analysis as well as the proofs of main results. In Section S3, we represent more simulation results. In Section S4, we give an example of application to Linear Discriminant Analysis. Finally, in Section S5, we prove lemmas and theorems of the main paper.

K Lee, K Lee, J Lee · 학술지 미등록 · 2022

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We consider high-dimensional multivariate linear regression models, where the joint distribution of covariates and response variables is a multivariate normal distribution with a bandable covariance matrix. The main goal of this paper is to estimate the regression coefficient matrix, which is a function of the bandable covariance matrix. Although the tapering estimator of covariance has the minimax optimal convergence rate for the class of bandable covariances, we show that it is sub-optimal for the regression coefficient; that is, a minimax estimator for the class of bandable covariances may not be a minimax estimator for its functionals. We propose the blockwise tapering estimator of the regression coefficient, which has the minimax optimal convergence rate for the regression coefficient under the bandable covariance assumption. We also propose a Bayesian procedure called the blockwise tapering post-processed …

K Lee, K Lee, J Lee · Electronic Journal of Statistics · 2022

인용 4회

In 2020, Korea Disease Control and Prevention Agency reported three rounds of surveys on seroprevalence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) antibodies in South Korea. SARS-CoV-2 is the virus which inflicts the coronavirus disease 2019 (COVID-19). We analyze the seroprevalence surveys using a Bayesian method with an informative prior distribution on the seroprevalence parameter, and the sensitivity and specificity of the diagnostic test. We construct the informative prior of the sensitivity and specificity of the diagnostic test using the posterior distribution obtained from the clinical evaluation data. The constraint of the seroprevalence parameter induced from the known confirmed coronavirus 2019 cases can be imposed naturally in the proposed Bayesian model. We also prove that the confidence interval of the seroprevalence parameter based on the Rao’s test can be the empty set …

K Lee, S Jo, J Lee · Journal of the Korean Statistical Society · 2021

인용 12회

We consider Bayesian inference of sparse covariance matrices and propose a post-processed posterior. This method consists of two steps. In the first step, posterior samples are obtained from the conjugate inverse-Wishart posterior without considering the sparse structural assumption. The posterior samples are transformed in the second step to satisfy the sparse structural assumption through the hard-thresholding function. This non-traditional Bayesian procedure is justified by showing that the post-processed posterior attains the optimal minimax rates. We also investigate the application of the post-processed posterior to the estimation of the global minimum variance portfolio. We show that the post-processed posterior for the global minimum variance portfolio also attains the optimal minimax rate under the sparse covariance assumption. The advantages of the post-processed posterior for the global minimum variance portfolio are demonstrated by a simulation study and a real data analysis with S&P 400 data.

K Lee, J Lee · arXiv preprint arXiv:2108.09462 · 2021

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The Indian Buffet Process is a stochastic process on equivalence classes of binary matrices having finite rows and infinite columns. The Indian Buffet Process can be imposed as the prior distribution on the binary matrix in an infinite feature model. We describe the derivation of the Indian buffet process from a finite feature model, and briefly explain the relation between the Indian buffet process and the beta process. Using a Gaussian linear model, we describe three algorithms: Gibbs sampling algorithm, Stick-breaking algorithm and variational method, with application for finding features in image data. We also illustrate the use of the Indian Buffet Process in various type of analysis such as dyadic data analysis, network data analysis and independent component analysis.

Y Leea, K Leea, K Leea, J Leea, J Seob · Korean Journal of Applied Statistics · 2015

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인도부페 프로세스는 유한개의 행과 무한개의 열로 이루어진 이진행렬의 분포와 관련된 확률과정이다. 무한특성모형을 유한개의 행과 무한개의 열로 이루어진 이진행렬을 이용해서 표현할 때, 이진행렬에 대한 사전분포로써 인도부페 프로세스가 이용될 수 있다. 본 논문에서는 인도부페 프로세스를 유한특성모형과 연관지어서 유도하는 방법을 소개하고, 베타프로세스와의 관련성을 간략히 설명한다. 실제 모형의 추론에 인도부페 프로세스가 이용되는 예제를 살펴보기 위해서 가우시안 선형모형에 인도부페 프로세스를 적용한 모형화 방법을 언급하고, 깁스표집 알고리즘, 막대 자르기 알고리즘, 변분방법을 이용한 추론방법을 설명한다. 그리고 이 세 가지 알고리즘을 이용하여 이미지 자료를 분석하는데 적용해본다. 나아가 쌍자료 분석, 네트워크 분석, 독립성분 분석에서 인도부페 프로세스가 어떻게 이용될 수 있는지도 알아본다.

이영선， 이경재， 이광민， 이재용， 서진욱 · 응용통계연구= The Korean journal of applied statistics · 2015

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