• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.251-267
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• 2015

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.

• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.315-334
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• 2005

The purpose of this study is to find out the implications on when and how the correlation concept can be taught. we investigate the development time and method of the concept in a statistical perspective those initially have discussed in psychology by Piaget. We first reviewed the 1958 research by Inhelder and Piaget. It was the first one which researched the development of the correlation and has become the foundation of psychological perspective. According to them, the correlation concept needs proportional and probability concept ahead of its development and argued on the coefficient of correlation based on formal and logical position. However, from a statistical perspective, the correlation concept is a part of the distribution concept. So, the level of the correlation concept grows from the comparison of conditional distributions to the conditional probability distribution where the proportional concept and probability concept are applied. As reviewed through the literature, we found that 11-12 years old students in early formal operation stage reasoned about correlation through the comparison of conditional distributions. In our study, we argue that we need to consider the possibility of beginning didactic mediation for correlation concept earlier and the method approaching it in a distribution perspective.

• Journal of the Korean Institute of Gas
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• v.1 no.1
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• pp.81-86
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• 1997

This study is to estimate the possibility of accident in chemical plants from the analysis of system component which affects the occurrence of top event. Among the various risk assessment techniques, the Fault Tree Analysis which approaches deductively on the route of accident development was used in this study. By gate-by-gate method and minimal cut set, the qualitative and quantitative risk assessment for hazards in plants was performed. The probability of occurrence and frequency of top event was calculated from failure or reliability data of system components at stage of the quantitative risk assessment. In conclusion, the probability of accident was estimated according to logic pattern based on the Fault Tree Analysis. And the failure path which mostly influences on the occurrence of top event was found from Importance Analysis.

• Water for future
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• v.27 no.4
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• pp.135-143
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• 1994

The purpose of this study was to improve the understanding of the characteristics of the daily urban water use. The city of Kwangju in Korea was selected as a study area. The population of Kwangju in the end of 1993 was more than one million and two hundred thousand peoples. The average of daily water use in 1993 was about three hundred and fifty thousand tons a day. The variation of the urban water demand trend with time for a day was studied. One day was devided into 12 divisions with a 2hour increment. The water use demand for the given time interval of a day was observed. The water use index was defind in percentage that indicates the ratio of the amount of water use for a time interval to the amount of water use for a day. The water use index was found to be useful to manage and to operate the water supply systems. In addition to this, the probability distribution of the water use demand for each time interval was tested using the K-S(Komogorov-Smirnov) method. The normal distribution type was found to be appropriate as the probability distribution type for the variation of water demand for the given time interval of a day.

• Journal of the Korean Data and Information Science Society
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• v.28 no.1
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• pp.153-161
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• 2017

Branching processes which is used for epidemic dispersion as stochastic process model have advantages to estimate parameters by real data. We have to estimate both mean and dispersion parameter in order to use the negative binomial distribution as an offspring distribution on branching processes. In existing studies on biology and epidemiology, it is estimated using maximum-likelihood methods. However, for most of epidemic data, it is hard to get the best precision of maximum-likelihood estimator. We suggest a Bayesian inference that have good properties of statistics for small-sample. After estimating dispersion parameter we modelled the posterior distribution for 2015 Korea MERS cases. As the result, we found that the estimated dispersion parameter is relatively stable no matter how we assume prior distribution. We also computed extinction probabilities on branching processes using estimated dispersion parameters.

• KIISE Transactions on Computing Practices
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• v.21 no.1
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• pp.94-99
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• 2015

With the recent machine learning paradigm of using nonparametric Bayesian statistics and statistical inference based on random sampling, the Dirichlet distribution finds many uses in a variety of graphical models. It is a multivariate generalization of the gamma distribution and is defined on a continuous (K-1)-simplex. This paper presents a sampling method for a Dirichlet distribution for the problem of dividing an integer X into a sequence of K integers which sum to X. The target samples in our problem are all positive integer vectors when multiplied by a given X. They must be sampled from the correspondingly gridded simplex. In this paper we develop a Markov Chain Monte Carlo (MCMC) proposal distribution for the neighborhood grid points on the simplex and then present the complete algorithm based on the Metropolis-Hastings algorithm. The proposed algorithm can be used for the Markov model, HMM, and Semi-Markov model for accurate state-duration modeling. It can also be used for the Gamma-Dirichlet HMM to model q the global-local duration distributions.

• Journal of Korean Tunnelling and Underground Space Association
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• v.20 no.4
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• pp.701-715
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• 2018

A reliability based design approach of the tunnel reinforcement with umbrella arch method was considered to better represent the uncertainties of the weak rock properties around the tunnel. For this, a machine learning approach called an Adaptive Support Vector Machine (ASVM) together with the limit equilibrium method were introduced to minimize the iteration numbers during the classification training of the tunnel stability. The proposed method was compared with the results of typical Monte Carlo simulations. It was concluded that the ASVM was very efficient and accurate to calculate the probability of failure having auxiliary umbrella arches and uncertain material properties of the tunnel. Future work will be concentrated on the refinement of the fast adaptation of the SVM classification so that the minimum number of numerical analyses can be used where the limit solution is not available.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.503-523
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• 2010

The current mathematics curriculum are consist of the following domains: 'Characteristics', 'Objectives', 'Contents', 'Teaching and learning method', and 'Assessment'. The mathematics standards which students have to learn in the school are presented in the domain of 'Contents'. 'Contents' are consist of the following sub-domains: 'Number and Operation', 'Geometric Figures', 'Measures', 'Probability and Statistics', and 'Pattern and Problem-Solving' (Elementary School); 'Number and Operation', 'Geometry', 'Letter and Formula', 'Function', and 'Probability and Statistics' (Junior and Senior High School). These sub-domains of 'Contents' are dealing with mathematical subjects, except 'Problem-Solving' at the elementary school level. In this study, the sub-domain of 'mathematical process' was suggested in an equal position to the typical sub-domains of 'Contents'.

• Korean Journal of Construction Engineering and Management
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• v.19 no.3
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• pp.33-42
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• 2018

In the aftermath of an earthquake, seismic-damaged infrastructure systems loss estimation is the first step for the disaster response. However, lifeline systems' ability to supply service can be volatile by external factors such as disturbances of nearby facilities, and not by own physical issue. Thus, this research develops the bayesian model for probabilistic inference on common-cause and cascading failure of seismic-damaged lifeline systems. In addition, the authors present network robustness estimation metrics in the context of failure propagation. In order to quantify the functional loss and observe the effect of the mitigation plan, power and water supply system in Daegu-Gyeongbuk in South Korea is selected as case network. The simulation results show that reduction of cascading failure probability allows withstanding the external disruptions from a perspective of the robustness improvement. This research enhances the comprehensive understanding of how a single failure propagates to whole lifeline system performance and affected region after an earthquake.

• The Korean Journal of Applied Statistics
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• v.20 no.3
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• pp.541-550
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• 2007

One of main aspects of time series analysis is to forecast future values of series based on values up to a given time. The prediction interval for future values is usually obtained under the normality assumption. When the assumption is seriously violated, a transformation of data may permit the valid use of the normal theory. We investigate the prediction problem for future values in the original scale when transformations are applied in ARMA models. In this paper, we introduce the methodology based on Yeo-Johnson transformation to solve the problem of skewed data whose modelling is relatively difficult in the analysis of time series. Simulation studies show that the coverage probabilities of proposed intervals are closer to the nominal level than those of usual intervals.