arXiv subjects

Taeryon Choi

Publications and source records attributed to Taeryon Choi.

5 recordsLinked to original sources

arXiv2024

Predicting COVID-19 hospitalisation using a mixture of Bayesian predictive syntheses

This paper proposes a novel methodology called the mixture of Bayesian predictive syntheses (MBPS) for multiple time series count data for the challenging task of predicting the numbers of COVID-19 inpatients and isolated cases in Japan and Korea at the subnational-level. MBPS combines a set of predictive models and partitions the multiple time series into clusters based on their contribution to predicting the outcome. In this way, MBPS leverages the shared information within each cluster and is suitable for predicting COVID-19 inpatients since the data exhibit similar dynamics over multiple areas. Also, MBPS avoids using a multivariate count model, which is generally cumbersome to develop and implement. Our Japanese and Korean data analyses demonstrate that the proposed MBPS methodology has improved predictive accuracy and uncertainty quantification.

stat.AP↗

arXiv2020

Use of Cross-validation Bayes Factors to Test Equality of Two Densities

We propose a non-parametric, two-sample Bayesian test for checking whether or not two data sets share a common distribution. The test makes use of data splitting ideas and does not require priors for high-dimensional parameter vectors as do other nonparametric Bayesian procedures. We provide evidence that the new procedure provides more stable Bayes factors than do methods based on Pólya trees. Somewhat surprisingly, the behavior of the proposed Bayes factors when the two distributions are the same is usually superior to that of Pólya tree Bayes factors. We showcase the effectiveness of the test by proving its consistency, conducting a simulation study and applying the test to Higgs boson data.

stat.ME↗

arXiv2016

Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian-Wishart processes

Functional data are defined as realizations of random functions (mostly smooth functions) varying over a continuum, which are usually collected with measurement errors on discretized grids. In order to accurately smooth noisy functional observations and deal with the issue of high-dimensional observation grids, we propose a novel Bayesian method based on the Bayesian hierarchical model with a Gaussian-Wishart process prior and basis function representations. We first derive an induced model for the basis-function coefficients of the functional data, and then use this model to conduct posterior inference through Markov chain Monte Carlo. Compared to the standard Bayesian inference that suffers serious computational burden and unstableness for analyzing high-dimensional functional data, our method greatly improves the computational scalability and stability, while inheriting the advantage of simultaneously smoothing raw observations and estimating the mean-covariance functions in a nonparametric way. In addition, our method can naturally handle functional data observed on random or uncommon grids. Simulation and real studies demonstrate that our method produces similar results as the standard Bayesian inference with low-dimensional common grids, while efficiently smoothing and estimating functional data with random and high-dimensional observation grids where the standard Bayesian inference fails. In conclusion, our method can efficiently smooth and estimate high-dimensional functional data, providing one way to resolve the curse of dimensionality for Bayesian functional data analysis with Gaussian-Wishart processes.

stat.ME↗

arXiv2015

Smoothing and mean-covariance estimation of functional data with a Bayesian hierarchical model

Functional data, with basic observational units being functions (e.g., curves, surfaces) varying over a continuum, are frequently encountered in various applications. While many statistical tools have been developed for functional data analysis, the issue of smoothing all functional observations simultaneously is less studied. Existing methods often focus on smoothing each individual function separately, at the risk of removing important systematic patterns common across functions. We propose a nonparametric Bayesian approach to smooth all functional observations simultaneously and nonparametrically. In the proposed approach, we assume that the functional observations are independent Gaussian processes subject to a common level of measurement errors, enabling the borrowing of strength across all observations. Unlike most Gaussian process regression models that rely on pre-specified structures for the covariance kernel, we adopt a hierarchical framework by assuming a Gaussian process prior for the mean function and an Inverse-Wishart process prior for the covariance function. These prior assumptions induce an automatic mean-covariance estimation in the posterior inference in addition to the simultaneous smoothing of all observations. Such a hierarchical framework is flexible enough to incorporate functional data with different characteristics, including data measured on either common or uncommon grids, and data with either stationary or nonstationary covariance structures. Simulations and real data analysis demonstrate that, in comparison with alternative methods, the proposed Bayesian approach achieves better smoothing accuracy and comparable mean-covariance estimation results. Furthermore, it can successfully retain the systematic patterns in the functional observations that are usually neglected by the existing functional data analyses based on individual-curve smoothing.

stat.ME↗

arXiv2008

Remarks on consistency of posterior distributions

In recent years, the literature in the area of Bayesian asymptotics has been rapidly growing. It is increasingly important to understand the concept of posterior consistency and validate specific Bayesian methods, in terms of consistency of posterior distributions. In this paper, we build up some conceptual issues in consistency of posterior distributions, and discuss panoramic views of them by comparing various approaches to posterior consistency that have been investigated in the literature. In addition, we provide interesting results on posterior consistency that deal with non-exponential consistency, improper priors and non i.i.d. (independent but not identically distributed) observations. We describe a few examples for illustrative purposes.

math.ST↗