• 대한수학회지
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• 제35권2호
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• pp.433-447
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• 1998

We investigate coboundary conditions for two functions defined on a mixing subshift of finite type to have the same Gibbs measure. Also we find conditions for a function to be a coboundary.

• 대한수학회지
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• 제34권3호
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• pp.731-770
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• 1997

We study Diriclet forms and related subjects for the Gibbs measures of classical unbounded sping systems interacting via potentials which are superstable and regular. For any Gibbs measure $\mu$, we construct a Dirichlet form and the associated diffusion process on $L^2(\Omega, d\mu), where \Omega = (R^d)^Z^\nu$. Under appropriate conditions on the potential we show that the Dirichlet operator associated to a Gibbs measure $\mu$ is essentially self-adjoint on the space of smooth bounded cylinder functions. Under the condition of uniform log-concavity, the Gibbs measure exists uniquely and there exists a mass gap in the lower end of the spectrum of the Dirichlet operator. We also show that under the condition of uniform log-concavity, the unique Gibbs measure satisfies the log-Sobolev inequality. We utilize the general scheme of the previous works on the theory in infinite dimensional spaces developed by e.g., Albeverio, Antonjuk, Hoegh-Krohn, Kondratiev, Rockner, and Kusuoka, etc, and also use the equilibrium condition and the regularity of Gibbs measures extensively.

• 대한수학회보
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• 제61권4호
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• pp.1087-1105
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• 2024

In this paper, we study a relation between the existence of invariant Gibbs measures and the balanced property of subshifts. We show that a subshift X has an invariant Gibbs measure for f ∈ C (X, ℝ) if and only if it is balanced with respect to f.

• 대한수학회지
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• 제33권4호
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• pp.823-855
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• 1996

We study Dirichlet forms and the associated diffusion processes for the Gibbs measures related to the quantum unbounded spin systems (lattice boson systems) interacting via superstable and regular potentials. This work is a continuation of the author's previous study on the classical systems [LPY] to the quantum cases. In [LPY], we constructed Dirichlet forms and the associated diffusion processes for the Gibbs measures of classical unbounded spin systems. Furthermore, we also showed the essential self-adjointness of the Dirichlet operator and the log-Sobolev inequality for any Gibbs measure under appropriate conditions on the potentials. In this atudy we try to extend the results of the classical systems to the quantum cases. Because of some technical difficulties, we are only able to construct a Dirichlet form and the associated diffusion process for any Gibbs measure of the quantum systems. We utilize the general scheme of the previous work on the theory in infinite dimensional spaces [AH-K1-2, AKR, AR1-2, Kus, MR, Ro, Sch] and the ideas we employed in our study of the calssical systems ]LPY].

• 대한수학회보
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• 제41권2호
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• pp.269-274
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• 2004

We investigate a deranged Cantor set (a generalized Cantor set) using the similar method to find the dimensions of cookie-cutter repeller. That is, we will use a Gibbs measure which is a weak limit of a subsequence of discrete Borel measures to find the dimensions. The deranged Cantor set that will be considered is a generalized form of a perturbed Cantor set (a variation of the symmetric Cantor set) and a cookie-cutter repeller.

• 응용통계연구
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• 제7권2호
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• pp.9-19
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• 1994

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.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 1998년도 The 12th Asia Quality Management Symposium* Total Quality Management for Restoring Competitiveness
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• pp.225-232
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• 1998

A Markov Chain Monte Carlo method with data augmentation is developed to compute the features of the posterior distribution. This data augmentation approach facilitates the specification of the transitional measure in the Markov Chain. Bayesian analysis of the mixture exponential model discusses using the Gibbs sampler. Parameter and reliability estimators are obtained. A numerical study is provided.

• Structural Engineering and Mechanics
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• 제87권1호
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• pp.1-18
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• 2023

The paper presents a Bayesian Finite element (FE) model updating methodology by utilizing modal data. The dynamic condensation technique is adopted in this work to reduce the full system model to a smaller model version such that the degrees of freedom (DOFs) in the reduced model correspond to the observed DOFs, which facilitates the model updating procedure without any mode-matching. The present work considers both the MPV and the covariance matrix of the modal parameters as the modal data. Besides, the modal data identified from multiple setups is considered for the model updating procedure, keeping in view of the realistic scenario of inability of limited number of sensors to measure the response of all the interested DOFs of a large structure. A relationship is established between the modal data and structural parameters based on the eigensystem equation through the introduction of additional uncertain parameters in the form of modal frequencies and partial mode shapes. A novel sampling strategy known as the Metropolis-within-Gibbs (MWG) sampler is proposed to sample from the posterior Probability Density Function (PDF). The effectiveness of the proposed approach is demonstrated by considering both simulated and experimental examples.

• 응용통계연구
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• 제13권2호
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• pp.505-514
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• 2000

마코브체인 몬테칼로방법중에서 깁스 추출방법을 혼합 고장모형에 이용하였다. 베이자안 추론에서 조건부분포를 가지고 사후 분포를 결정하는데 있어서 계산 문제와 이론적인 정당성을 고려하여 감마족인 Rayleigh와 Erlang추세를 가진 혼합모형에 대하여 깁스샘플링 알고리즘을 이용하여 베이지안 계산과 신뢰도 추이를 알아보고 모의실험자료를 이용하여 수치적인 계산을 시행하고 그 결과를 제시하였다.

• 대한수학회논문집
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• 제13권4호
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• pp.691-725
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• 1998

무한차원 상공간에서의 디리클레 형식과 이에 관계된 확산과정에 대한 일반 이론을 소개하고, 이 이론을 물리학의 통계역학 모델에 적용하였다. 구체적으로, 고전 비유계 스핀계에 대한 통계역학적인 모델, 연속체 공간에서 상호 작용하는 무한 입자계에 대한 통계역학적인 모델에 응용하였다. 아울러서 확률 미분 방정식과 같은 디리클레 형식에 관련된 연구분야에 대해서도 간단히 알아보았다.