arXiv subjects

Guanyu Hu

Publications and source records attributed to Guanyu Hu.

At least 55 records · Page 3Linked to original sources

arXiv2021

Bayesian Variable Selection for Cox Regression Model with Spatially Varying Coefficients with Applications to Louisiana Respiratory Cancer Data

The Cox regression model is a commonly used model in survival analysis. In public health studies, clinical data are often collected from medical service providers of different locations. There are large geographical variations in the covariate effects on survival rates from particular diseases. In this paper, we focus on the variable selection issue for the Cox regression model with spatially varying coefficients. We propose a Bayesian hierarchical model which incorporates a horseshoe prior for sparsity and a point mass mixture prior to determine whether a regression coefficient is spatially varying. An efficient two-stage computational method is used for posterior inference and variable selection. It essentially applies the existing method for maximizing the partial likelihood for the Cox model by site independently first, and then applying an MCMC algorithm for variable selection based on results of the first stage. Extensive simulation studies are carried out to examine the empirical performance of the proposed method. Finally, we apply the proposed methodology to analyzing a real data set on respiratory cancer in Louisiana from the SEER program.

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arXiv2021

Bayesian Spatial Homogeneity Pursuit of Functional Data: an Application to the U.S. Income Distribution

An income distribution describes how an entity's total wealth is distributed amongst its population. A problem of interest to regional economics researchers is to understand the spatial homogeneity of income distributions among different regions. In economics, the Lorenz curve is a well-known functional representation of income distribution. In this article, we propose a mixture of finite mixtures (MFM) model as well as a Markov random field constrained mixture of finite mixtures (MRFC-MFM) model in the context of spatial functional data analysis to capture spatial homogeneity of Lorenz curves. We design efficient Markov chain Monte Carlo (MCMC) algorithms to simultaneously infer the posterior distributions of the number of clusters and the clustering configuration of spatial functional data. Extensive simulation studies are carried out to show the effectiveness of the proposed methods compared with existing methods. We apply the proposed spatial functional clustering method to state level income Lorenz curves from the American Community Survey Public Use Microdata Sample (PUMS) data. The results reveal a number of important clustering patterns of state-level income distributions across US.

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arXiv2021

Zero Inflated Poisson Model with Clustered Regression Coefficients: an Application to Heterogeneity Learning of Field Goal Attempts of Professional Basketball Players

Although basketball is a dynamic process sport, with 5 plus 5 players competing on both offense and defense simultaneously, learning some static information is predominant for professional players, coaches and team mangers. In order to have a deep understanding of field goal attempts among different players, we propose a zero inflated Poisson model with clustered regression coefficients to learn the shooting habits of different players over the court and the heterogeneity among them. Specifically, the zero inflated model recovers the large proportion of the court with zero field goal attempts, and the mixture of finite mixtures model learn the heterogeneity among different players based on clustered regression coefficients and inflated probabilities. Both theoretical and empirical justification through simulation studies validate our proposed method. We apply our proposed model to the National Basketball Association (NBA), for learning players' shooting habits and heterogeneity among different players over the 2017--2018 regular season. This illustrates our model as a way of providing insights from different aspects.

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arXiv2021

Time Fused Coefficient SIR Model with Application to COVID-19 Epidemic in the United States

In this paper, we propose a Susceptible-Infected-Removal (SIR) model with time fused coefficients. In particular, our proposed model discovers the underlying time homogeneity pattern for the SIR model's transmission rate and removal rate via Bayesian shrinkage priors. MCMC sampling for the proposed method is facilitated by the nimble package in R. Extensive simulation studies are carried out to examine the empirical performance of the proposed methods. We further apply the proposed methodology to analyze different levels of COVID-19 data in the United States.

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arXiv2021

Bayesian Spatial Homogeneity Pursuit for Survival Data with an Application to the SEER Respiratory Cancer Data

In this work, we propose a new Bayesian spatial homogeneity pursuit method for survival data under the proportional hazards model to detect spatially clustered patterns in baseline hazard and regression coefficients. Specially, regression coefficients and baseline hazard are assumed to have spatial homogeneity pattern over space. To capture such homogeneity, we develop a geographically weighted Chinese restaurant process prior to simultaneously estimate coefficients and baseline hazards and their uncertainty measures. An efficient Markov chain Monte Carlo (MCMC) algorithm is designed for our proposed methods. Performance is evaluated using simulated data, and further applied to a real data analysis of respiratory cancer in the state of Louisiana.

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arXiv2020

A Bayesian marked spatial point processes model for basketball shot chart

The success rate of a basketball shot may be higher at locations where a player makes more shots. For a marked spatial point process, this means that the mark and the intensity are associated. We propose a Bayesian joint model for the mark and the intensity of marked point processes, where the intensity is incorporated in the mark model as a covariate. Inferences are done with a Markov chain Monte Carlo algorithm. Two Bayesian model comparison criteria, the Deviance Information Criterion and the Logarithm of the Pseudo-Marginal Likelihood, were used to assess the model. The performances of the proposed methods were examined in extensive simulation studies. The proposed methods were applied to the shot charts of four players (Curry, Harden, Durant, and James) in the 2017--2018 regular season of the National Basketball Association to analyze their shot intensity in the field and the field goal percentage in detail. Application to the top 50 most frequent shooters in the season suggests that the field goal percentage and the shot intensity are positively associated for a majority of the players. The fitted parameters were used as inputs in a secondary analysis to cluster the players into different groups.

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arXiv2020

Identifying latent groups in spatial panel data using a Markov random field constrained product partition model

Understanding the heterogeneity over spatial locations is an important problem that has been widely studied in many applications such as economics and environmental science. In this paper, we focus on regression models for spatial panel data analysis, where repeated measurements are collected over time at various spatial locations. We propose a novel class of nonparametric priors that combines Markov random field (MRF) with the product partition model (PPM), and show that the resulting prior, called by MRF-PPM, is capable of identifying the latent group structure among the spatial locations while efficiently utilizing the spatial dependence information. We derive a closed-form conditional distribution for the proposed prior and introduce a new way to compute the marginal likelihood that renders efficient Bayesian inference. We further study the theoretical properties of the proposed MRF-PPM prior and show a clustering consistency result for the posterior distribution. We demonstrate the excellent empirical performance of our method via extensive simulation studies and applications to a US precipitation data and a California median household income data study.

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arXiv2020

Bayesian Nonparametric Estimation for Point Processes with Spatial Homogeneity: A Spatial Analysis of NBA Shot Locations

Basketball shot location data provide valuable summary information regarding players to coaches, sports analysts, fans, statisticians, as well as players themselves. Represented by spatial points, such data are naturally analyzed with spatial point process models. We present a novel nonparametric Bayesian method for learning the underlying intensity surface built upon a combination of Dirichlet process and Markov random field. Our method has the advantage of effectively encouraging local spatial homogeneity when estimating a globally heterogeneous intensity surface. Posterior inferences are performed with an efficient Markov chain Monte Carlo (MCMC) algorithm. Simulation studies show that the inferences are accurate and that the method is superior compared to the competing methods. Application to the shot location data of $20$ representative NBA players in the 2017-2018 regular season offers interesting insights about the shooting patterns of these players. A comparison against the competing method shows that the proposed method can effectively incorporate spatial contiguity into the estimation of intensity surfaces.

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arXiv2020

Bayesian Group Learning for Shot Selection of Professional Basketball Players

In this paper, we develop a group learning approach to analyze the underlying heterogeneity structure of shot selection among professional basketball players in the NBA. We propose a mixture of finite mixtures (MFM) model to capture the heterogeneity of shot selection among different players based on Log Gaussian Cox process (LGCP). Our proposed method can simultaneously estimate the number of groups and group configurations. An efficient Markov Chain Monte Carlo (MCMC) algorithm is developed for our proposed model. Simulation studies have been conducted to demonstrate its performance. Ultimately, our proposed learning approach is further illustrated in analyzing shot charts of several players in the NBA's 2017-2018 regular season.

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arXiv2020

Analysis of professional basketball field goal attempts via a Bayesian matrix clustering approach

We propose a Bayesian nonparametric matrix clustering approach to analyze the latent heterogeneity structure in the shot selection data collected from professional basketball players in the National Basketball Association (NBA). The proposed method adopts a mixture of finite mixtures framework and fully utilizes the spatial information via a mixture of matrix normal distribution representation. We propose an efficient Markov chain Monte Carlo algorithm for posterior sampling that allows simultaneous inference on both the number of clusters and the cluster configurations. We also establish large sample convergence properties for the posterior distribution. The excellent empirical performance of the proposed method is demonstrated via simulation studies and an application to shot chart data from selected players in the 2017 18 NBA regular season.

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arXiv2020

Spatial homogeneity learning for spatially correlated functional data with application to COVID-19 Growth rate curves

We study the spatial heterogeneity effect on regional COVID-19 pandemic timing and severity by analyzing the COVID-19 growth rate curves in the United States. We propose a geographically detailed functional data grouping method equipped with a functional conditional autoregressive (CAR) prior to fully capture the spatial correlation in the pandemic curves. The spatial homogeneity pattern can then be detected by a geographically weighted Chinese restaurant process prior which allows both locally spatially contiguous groups and globally discontiguous groups. We design an efficient Markov chain Monte Carlo (MCMC) algorithm to simultaneously infer the posterior distributions of the number of groups and the grouping configuration of spatial functional data. The superior numerical performance of the proposed method over competing methods is demonstrated using simulated studies and an application to COVID-19 state-level and county-level data study in the United States.

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arXiv2020

Heterogeneity Learning for SIRS model: an Application to the COVID-19

We propose a Bayesian Heterogeneity Learning approach for Susceptible-Infected-Removal-Susceptible (SIRS) model that allows underlying clustering patterns for transmission rate, recovery rate, and loss of immunity rate for the latest coronavirus (COVID-19) among different regions. Our proposed method provides simultaneously inference on parameter estimation and clustering information which contains both number of clusters and cluster configurations. Specifically, our key idea is to formulates the SIRS model into a hierarchical form and assign the Mixture of Finite mixtures priors for heterogeneity learning. The properties of the proposed models are examined and a Markov chain Monte Carlo sampling algorithm is used to sample from the posterior distribution. Extensive simulation studies are carried out to examine empirical performance of the proposed methods. We further apply the proposed methodology to analyze the state level COVID-19 data in U.S.

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arXiv2020

Geographically Weighted Regression Analysis for Spatial Economics Data: a Bayesian Recourse

The geographically weighted regression (GWR) is a well-known statistical approach to explore spatial non-stationarity of the regression relationship in spatial data analysis. In this paper, we discuss a Bayesian recourse of GWR. Bayesian variable selection based on spike-and-slab prior, bandwidth selection based on range prior, and model assessment using a modified deviance information criterion and a modified logarithm of pseudo-marginal likelihood are fully discussed in this paper. Usage of the graph distance in modeling areal data is also introduced. Extensive simulation studies are carried out to examine the empirical performance of the proposed methods with both small and large number of location scenarios, and comparison with the classical frequentist GWR is made. The performance of variable selection and estimation of the proposed methodology under different circumstances are satisfactory. We further apply the proposed methodology in analysis of a province-level macroeconomic data of 30 selected provinces in China. The estimation and variable selection results reveal insights about China's economy that are convincing and agree with previous studies and facts.

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arXiv2020

Bayesian Hierarchical Spatial Regression Models for Spatial Data in the Presence of Missing Covariates with Applications

In many applications, survey data are collected from different survey centers in different regions. It happens that in some circumstances, response variables are completely observed while the covariates have missing values. In this paper, we propose a joint spatial regression model for the response variable and missing covariates via a sequence of one-dimensional conditional spatial regression models. We further construct a joint spatial model for missing covariate data mechanisms. The properties of the proposed models are examined and a Markov chain Monte Carlo sampling algorithm is used to sample from the posterior distribution. In addition, the Bayesian model comparison criteria, the modified Deviance Information Criterion (mDIC) and the modified Logarithm of the Pseudo-Marginal Likelihood (mLPML), are developed to assess the fit of spatial regression models for spatial data. Extensive simulation studies are carried out to examine empirical performance of the proposed methods. We further apply the proposed methodology to analyze a real data set from a Chinese Health and Nutrition Survey (CHNS) conducted in 2011.

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arXiv2020

A Nonparametric Bayesian Item Response Modeling Approach for Clustering Items and Individuals Simultaneously

Item response theory (IRT) is a popular modeling paradigm for measuring subject latent traits and item properties according to discrete responses in tests or questionnaires. There are very limited discussions on heterogeneity pattern detection for both items and individuals. In this paper, we introduce a nonparametric Bayesian approach for clustering items and individuals simultaneously under the Rasch model. Specifically, our proposed method is based on the mixture of finite mixtures (MFM) model. MFM obtains the number of clusters and the clustering configurations for both items and individuals simultaneously. The performance of parameters estimation and parameters clustering under the MFM Rasch model is evaluated by simulation studies, and a real date set is applied to illustrate the MFM Rasch modeling.

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arXiv2020

Most Likely Optimal Subsampled Markov Chain Monte Carlo

Markov Chain Monte Carlo (MCMC) requires to evaluate the full data likelihood at different parameter values iteratively and is often computationally infeasible for large data sets. In this paper, we propose to approximate the log-likelihood with subsamples taken according to nonuniform subsampling probabilities, and derive the most likely optimal (MLO) subsampling probabilities for better approximation. Compared with existing subsampled MCMC algorithm with equal subsampling probabilities, our MLO subsampled MCMC has a higher estimation efficiency with the same subsampling ratio. We also derive a formula using the asymptotic distribution of the subsampled log-likelihood to determine the required subsample size in each MCMC iteration for a given level of precision. This formula is used to develop an adaptive version of the MLO subsampled MCMC algorithm. Numerical experiments demonstrate that the proposed method outperforms the uniform subsampled MCMC.

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arXiv2020

Heterogeneous Regression Models for Clusters of Spatial Dependent Data

In economic development, there are often regions that share similar economic characteristics, and economic models on such regions tend to have similar covariate effects. In this paper, we propose a Bayesian clustered regression for spatially dependent data in order to detect clusters in the covariate effects. Our proposed method is based on the Dirichlet process which provides a probabilistic framework for simultaneous inference of the number of clusters and the clustering configurations. The usage of our method is illustrated both in simulation studies and an application to a housing cost dataset of Georgia.

econ.EM↗

arXiv2020

Heterogeneity Pursuit for Spatial Point Pattern with Application to Tree Locations: A Bayesian Semiparametric Recourse

Spatial point pattern data are routinely encountered. A flexible regression model for the underlying intensity is essential to characterizing the spatial point pattern and understanding the impacts of potential risk factors on such pattern. We propose a Bayesian semiparametric regression model where the observed spatial points follow a spatial Poisson process with an intensity function which adjusts a nonparametric baseline intensity with multiplicative covariate effects. The baseline intensity is piecewise constant, approached with a powered Chinese restaurant process prior which prevents an unnecessarily large number of pieces. The parametric regression part allows for variable selection through the spike-slab prior on the regression coefficients. An efficient Markov chain Monte Carlo (MCMC) algorithm is developed for the proposed methods. The performance of the methods is validated in an extensive simulation study. In application to the locations of Beilschmiedia pendula trees in the Barro Colorado Island forest dynamics research plot in central Panama, the spatial heterogeneity is attributed to a subset of soil measurements in addition to geographic measurements with a spatially varying baseline intensity.

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