Seongil Jo

Dependent Species Sampling Models for Spatial Density Estimation

We consider a novel Bayesian nonparametric model for density estimation with an underlying spatial structure. The model is built on a class of species sampling models, which are discrete random probability measures that can be represented as a mixture of random support points and random weights. Specifically, we construct a collection of spatially dependent species sampling models and propose a mixture model based on this collection. The key idea is the introduction of spatial dependence by modeling the weights through a conditional autoregressive model. We present an extensive simulation study to compare the performance of the proposed model with competitors. The proposed model compares favorably to these alternatives. We apply the method to the estimation of summer precipitation density functions using Climate Prediction Center Merged Analysis of Precipitation data over East Asia.

Bayesian Regression Model for Seasonal Forecast of Precipitation over Korea

In this paper, we apply three different Bayesian methods to the seasonal forecasting of the precipitation in a region around Korea (32.5°N–42.5°N, 122.5°E-132.5°E). We focus on the precipitation of summer season (June–July–August; JJA) for the period of 1979–2007 using the precipitation produced by the Global Data Assimilation and Prediction System (GDAPS) as predictors. Through cross-validation, we demonstrate improvement for seasonal forecast of precipitation in terms of root mean squared error (RMSE) and linear error in probability space score (LEPS). The proposed methods yield RMSE of 1.09 and LEPS of 0.31 between the predicted and observed precipitations, while the prediction using GDAPS output only produces RMSE of 1.20 and LEPS of 0.33 for CPC Merged Analyzed Precipitation (CMAP) data. For station-measured precipitation data, the RMSE and LEPS of the proposed Bayesian methods are 0.53 and 0.29, while GDAPS output is 0.66 and 0.33, respectively. The methods seem to capture the spatial pattern of the observed precipitation. The Bayesian paradigm incorporates the model uncertainty as an integral part of modeling in a natural way. We provide a probabilistic forecast integrating model uncertainty.

Spatial Species Sampling and Product Partition Models

Inference for spatial data arises, for example in medical imaging, epidemiology, ecology, and other areas, and gives rise to specific challenges for nonparametric Bayesian modeling. In this chapter we briefly review the fast growing related literature and discuss two specific models in more detail. The two models are the CAR SSM (species sampling with conditional autoregression) prior of Jo et al. (Dependent species sampling models for spatial density estimation. Technical report, Department of Statistics, Seoul National University, 2015) and the spatial PPM (product partition model) of Page and Quintana (Spatial product partition models. Technical report, Pontificia Universidad Catolica de Chile, 2015).

Bayesian spectral analysis models for quantile regression with Dirichlet process mixtures

This paper presents a Bayesian analysis of partially linear additive models for quantile regression. We develop a semiparametric Bayesian approach to quantile regression models using a spectral representation of the nonparametric regression functions and the Dirichlet process (DP) mixture for error distribution. We also consider Bayesian variable selection procedures for both parametric and nonparametric components in a partially linear additive model structure based on the Bayesian shrinkage priors via a stochastic search algorithm. Based on the proposed Bayesian semiparametric additive quantile regression model referred to as BSAQ, the Bayesian inference is considered for estimation and model selection. For the posterior computation, we design a simple and efficient Gibbs sampler based on a location-scale mixture of exponential and normal distributions for an asymmetric Laplace distribution, which facilitates the commonly used collapsed Gibbs sampling algorithms for the DP mixture models. Additionally, we discuss the asymptotic property of the sempiparametric quantile regression model in terms of consistency of posterior distribution. Simulation studies and real data application examples illustrate the proposed method and compare it with Bayesian quantile regression methods in the literature.

Prediction of East Asian summer precipitation via independent component analysis

A new statistical postprocessing method is proposed for seasonal climate prediction. The proposed method is based on a combination of independent component analysis (ICA) and canonical correlation analysis (CCA). Since the classical CCA cannot handle high-dimensional data wherein the number of variables is larger than the number of observations, ICA is pre-performed to reduce the dimension of the data. It is well known that empirical orthogonal function (EOF) analysis is a popular method for dimension reduction in the climatology community; however, loss of information occurs when the data is not Gaussian distributed. To extend the scope of distribution assumption and improve the prediction ability simultaneously, we propose the ICA-based method. This study focuses on the prediction of future precipitation for the boreal summer (June–July–August; JJA) through 29 years (1979–2007) on East Asia region. Results of the proposed ICA-based method show an improvement in seasonal climate prediction in terms of correlation and root mean square error as compared with those of the GCM simulation and the EOF/CCA method.

Climate Prediction by a Hybrid Method with Emphasizing Future Precipitation Change of East Asia

A canonical correlation analysis(CCA)-based method is proposed for prediction of future climate change which combines information from ensembles of atmosphere-ocean general circulation models(AOGCMs) and observed climate values. This paper focuses on predictions of future climate on a regional scale which are of potential economic values. The proposed method is obtained by coupling the classical CCA with empirical orthogonal functions(EOF) for dimension reduction. Furthermore, we generate a distribution of climate responses, so that extreme events as well as a general feature such as long tails and unimodality can be revealed through the distribution. Results from real data examples demonstrate the promising empirical properties of the proposed approaches.

Posterior convergence for Bayesian functional linear regression

We consider the asymptotic properties of Bayesian functional linear regression models where the response is a scalar and the predictor is a random function. Functional linear regression models have been routinely applied to many functional data analytic tasks in practice, and recent developments have been made in theory and methods. However, few works have investigated the frequentist convergence property of the posterior distribution of the Bayesian functional linear regression model. In this paper, we attempt to conduct a theoretical study to understand the posterior contraction rate in the Bayesian functional linear regression. It is shown that an appropriately chosen prior leads to the minimax rate in prediction risk.

Bayesian factor analysis with uncertain functional constraints about factor loadings

Factor analysis with uncertain functional constraints about factor loading matrix is considered from a Bayesian viewpoint, in which the uncertain prior information is incorporated in the analysis. We propose a hierarchical screened scale mixture of normal factor (HSMF) model for flexible inference of the constrained factor loadings, factor scores, and specific variances as well as the covariance matrix of the factors. The proposed model makes provisions for robust factor analysis with uncertainty about the functional constraints. A number of inferential aspects of the proposed model are investigated in order to render the proposed analysis optimal. These include the closure properties of a class of rectangle-screened scale mixture of multivariate normal ( R S M N ) distributions which is useful for statistical inference of the HSMF model, eliciting the prior and posterior evolutions of the uncertainly constrained factor loadings, and providing the efficient Bayesian estimation procedure by using the MCMC methods. Empirical analysis for Bayesian factor models with synthetic data and real data applications is given to illustrate the usefulness of the proposed model.

Bayesian variable selection approach to a Bernstein polynomial regression model with stochastic constraints

ABSTRACT This paper provides a Bayesian estimation procedure for monotone regression models incorporating the monotone trend constraint subject to uncertainty. For monotone regression modeling with stochastic restrictions, we propose a Bayesian Bernstein polynomial regression model using two-stage hierarchical prior distributions based on a family of rectangle-screened multivariate Gaussian distributions extended from the work of Gurtis and Ghosh [7]. This approach reflects the uncertainty about the prior constraint, and thus proposes a regression model subject to monotone restriction with uncertainty. Based on the proposed model, we derive the posterior distributions for unknown parameters and present numerical schemes to generate posterior samples. We show the empirical performance of the proposed model based on synthetic data and real data applications and compare the performance to the Bernstein polynomial regression model of Curtis and Ghosh [7] for the shape restriction with certainty. We illustrate the effectiveness of our proposed method that incorporates the uncertainty of the monotone trend and automatically adapts the regression function to the monotonicity, through empirical analysis with synthetic data and real data applications.

A Comparison Study of Bayesian Methods for a Threshold Autoregressive Model with Regime-Switching

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.