• 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 Korean Journal of Applied Statistics
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• v.35 no.3
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• pp.445-455
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• 2022

In this paper, we introduce existing Bayesian methods for high-dimensional sparse regression models and compare their performance in various simulation scenarios. Especially, we focus on the variational Bayes approach proposed by Ray and Szabó (2021), which enables scalable and accurate Bayesian inference. Based on simulated data sets from sparse high-dimensional linear regression models, we compare the variational Bayes approach with other Bayesian and frequentist methods. To check the practical performance of the variational Bayes in logistic regression models, a real data analysis is conducted using leukemia data set.

• The Korean Journal of Applied Statistics
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• v.36 no.2
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• pp.115-127
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• 2023

Multinomial probit model is a popular model for multiclass classification and choice model. Markov chain Monte Carlo (MCMC) method is widely used for estimating multinomial probit model, but its computational cost is high. However, it is well known that variational Bayesian approximation is more computationally efficient than MCMC, because it uses subsets of samples. In this study, we describe multinomial probit model with Gaussian process classification and how to employ variational Bayesian approximation on the model. This study also compares the results of variational Bayesian multinomial probit model to the results of naive Bayes, K-nearest neighbors and support vector machine for the UCI mice protein expression level data.