• The Korean Journal of Applied Statistics
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• v.34 no.1
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• pp.9-23
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• 2021

In the following paper we introduce a variational Bayes method that approximates posterior distributions with mean-field method. In particular, we introduce automatic differentiation variation inference (ADVI), which approximates joint posterior distributions using the product of Gaussian distributions after transforming parameters into real coordinate space, and then apply it to pharmacokinetic models that are models for the study of the time course of drug absorption, distribution, metabolism and excretion. We analyze real data sets using ADVI and compare the results with those based on Markov chain Monte Carlo. We implement the algorithms using Stan.

• The Journal of the Korea Contents Association
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• v.21 no.11
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• pp.77-86
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• 2021

A method of constructing a war simulation based on Bayesian Inference was proposed as a method of constructing heterogeneous historical war data obtained with a time difference into a single model. A method of applying a linear regression model can be considered as a method of predicting future battles by analyzing historical war results. However it is not appropriate for two heterogeneous types of historical data that reflect changes in the battlefield environment due to different times to be suitable as a single linear regression model and violation of the model's assumptions. To resolve these problems a Bayesian inference method was proposed to obtain a post-distribution by assuming the data from the previous era as a non-informative prior distribution and to infer the final posterior distribution by using it as a prior distribution to analyze the data obtained from the next era. Another advantage of the Bayesian inference method is that the results sampled by the Markov Chain Monte Carlo method can be used to infer posterior distribution or posterior predictive distribution reflecting uncertainty. In this way, it has the advantage of not only being able to utilize a variety of information rather than analyzing it with a classical linear regression model, but also continuing to update the model by reflecting additional data obtained in the future.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.1049-1068
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• 2014

Autoregressive models are used to analyze an univariate time series data; however, these methods can be inappropriate when a structural break appears in a time series since they assume that a trend is consistent. Threshold autoregressive models (popular regime-switching models) have been proposed to address this problem. Recently, the models have been extended to two regime-switching models with delay parameter. We discuss two regime-switching threshold autoregressive models from a Bayesian point of view. For a Bayesian analysis, we consider a parametric threshold autoregressive model and a nonparametric threshold autoregressive model using Dirichlet process prior. The posterior distributions are derived and the posterior inferences is performed via Markov chain Monte Carlo method and based on two Bayesian threshold autoregressive models. We present a simulation study to compare the performance of the models. We also apply models to gross domestic product data of U.S.A and South Korea.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.39 no.8
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• pp.751-758
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• 2015

Mathematical models are actively used to reduce the experimental expenses required to understand physical phenomena. However, they are different from real phenomena because of assumptions or uncertain parameters. In this study, we present a calibration and validation method using a paper helicopter and statistical methods to quantify the uncertainty. The data from the experiment using three nominally identical paper helicopters consist of different groups, and are used to calibrate the drag coefficient, which is an unknown input parameter in both analytical models. We predict the predicted fall time data using probability distributions. We validate the analysis models by comparing the predicted distribution and the experimental data distribution. Moreover, we quantify the uncertainty using the Markov Chain Monte Carlo method. In addition, we compare the manufacturing error and experimental error obtained from the fall-time data using Analysis of Variance. As a result, all of the paper helicopters are treated as one identical model.