arXiv subjects

Shonosuke Sugasawa

Publications and source records attributed to Shonosuke Sugasawa.

At least 73 records · Page 4Linked to original sources

arXiv2023

Fast and Locally Adaptive Bayesian Quantile Smoothing using Calibrated Variational Approximations

Quantiles are useful characteristics of random variables that can provide substantial information on distributions compared with commonly used summary statistics such as means. In this paper, we propose a Bayesian quantile trend filtering method to estimate non-stationary trend of quantiles. We introduce general shrinkage priors to induce locally adaptive Bayesian inference on trends and mixture representation of the asymmetric Laplace likelihood. To quickly compute the posterior distribution, we develop calibrated mean-field variational approximations to guarantee that the frequentist coverage of credible intervals obtained from the approximated posterior is a specified nominal level. Simulation and empirical studies show that the proposed algorithm is computationally much more efficient than the Gibbs sampler and tends to provide stable inference results, especially for high/low quantiles.

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arXiv2023

An Unbiased Predictor for Skewed Response Variable with Measurement Error in Covariate

We introduce a new small area predictor when the Fay-Herriot normal error model is fitted to a logarithmically transformed response variable, and the covariate is measured with error. This framework has been previously studied by Mosaferi et al. (2023). The empirical predictor given in their manuscript cannot perform uniformly better than the direct estimator. Our proposed predictor in this manuscript is unbiased and can perform uniformly better than the one proposed in Mosaferi et al. (2023). We derive an approximation of the mean squared error (MSE) for the predictor. The prediction intervals based on the MSE suffer from coverage problems. Thus, we propose a non-parametric bootstrap prediction interval which is more accurate. This problem is of great interest in small area applications since statistical agencies and agricultural surveys are often asked to produce estimates of right skewed variables with covariates measured with errors. With Monte Carlo simulation studies and two Census Bureau's data sets, we demonstrate the superiority of our proposed methodology.

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arXiv2023

Gibbs Sampler for Matrix Generalized Inverse Gaussian Distributions

Sampling from matrix generalized inverse Gaussian (MGIG) distributions is required in Markov Chain Monte Carlo (MCMC) algorithms for a variety of statistical models. However, an efficient sampling scheme for the MGIG distributions has not been fully developed. We here propose a novel blocked Gibbs sampler for the MGIG distributions, based on the Choleski decomposition. We show that the full conditionals of the diagonal and unit lower-triangular entries are univariate generalized inverse Gaussian and multivariate normal distributions, respectively. Several variants of the Metropolis-Hastings algorithm can also be considered for this problem, but we mathematically prove that the average acceptance rates become extremely low in particular scenarios. We demonstrate the computational efficiency of the proposed Gibbs sampler through simulation studies and data analysis.

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arXiv2022

Sparse Bayesian inference on gamma-distributed observations using shape-scale inverse-gamma mixtures

In various applications, we deal with high-dimensional positive-valued data that often exhibits sparsity. This paper develops a new class of continuous global-local shrinkage priors tailored to analyzing gamma-distributed observations where most of the underlying means are concentrated around a certain value. Unlike existing shrinkage priors, our new prior is a shape-scale mixture of inverse-gamma distributions, which has a desirable interpretation of the form of posterior mean and admits flexible shrinkage. We show that the proposed prior has two desirable theoretical properties; Kullback-Leibler super-efficiency under sparsity and robust shrinkage rules for large observations. We propose an efficient sampling algorithm for posterior inference. The performance of the proposed method is illustrated through simulation and two real data examples, the average length of hospital stay for COVID-19 in South Korea and adaptive variance estimation of gene expression data.

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arXiv2022

Dynamic Spatio-temporal Zero-inflated Poisson Models for Predicting Capelin Distribution in the Barents Sea

We consider modeling and prediction of Capelin distribution in the Barents sea based on zero-inflated count observation data that vary continuously over a specified survey region. The model is a mixture of two components; a one-point distribution at the origin and a Poisson distribution with spatio-temporal intensity, where both intensity and mixing proportions are modeled by some auxiliary variables and unobserved spatio-temporal effects. The spatio-temporal effects are modeled by a dynamic linear model combined with the predictive Gaussian process. We develop an efficient posterior computational algorithm for the model using a data augmentation strategy. The performance of the proposed model is demonstrated through simulation studies, and an application to the number of Capelin caught in the Barents sea from 2014 to 2019.

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arXiv2022

Functional Horseshoe Smoothing for Functional Trend Estimation

Due to developments in instruments and computers, functional observations are increasingly popular. However, effective methodologies for flexibly estimating the underlying trends with valid uncertainty quantification for a sequence of functional data (e.g. functional time series) are still scarce. In this work, we develop a locally adaptive smoothing method, called functional horseshoe smoothing, by introducing a shrinkage prior to the general order of differences of functional variables. This allows us to capture abrupt changes by making the most of the shrinkage capability and also to assess uncertainty by Bayesian inference. The fully Bayesian framework allows the selection of the number of basis functions via the posterior predictive loss. We provide theoretical properties of the model, which support the shrinkage ability. Also, by taking advantage of the nature of functional data, this method is able to handle heterogeneously observed data without data augmentation. Simulation studies and real data analysis demonstrate that the proposed method has desirable properties.

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arXiv2022

On Data Augmentation for Models Involving Reciprocal Gamma Functions

In this paper, we introduce a new and efficient data augmentation approach to the posterior inference of the models with shape parameters when the reciprocal gamma function appears in full conditional densities. Our approach is to approximate full conditional densities of shape parameters by using Gauss's multiplication formula and Stirling's formula for the gamma function, where the approximation error can be made arbitrarily small. We use the techniques to construct efficient Gibbs and Metropolis-Hastings algorithms for a variety of models that involve the gamma distribution, Student's $t$-distribution, the Dirichlet distribution, the negative binomial distribution, and the Wishart distribution. The proposed sampling method is numerically demonstrated through simulation studies.

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arXiv2022

Semiparametric imputation using latent sparse conditional Gaussian mixtures for multivariate mixed outcomes

This paper proposes a flexible Bayesian approach to multiple imputation using conditional Gaussian mixtures. We introduce novel shrinkage priors for covariate-dependent mixing proportions in the mixture models to automatically select the suitable number of components used in the imputation step. We develop an efficient sampling algorithm for posterior computation and multiple imputation via Markov Chain Monte Carlo methods. The proposed method can be easily extended to the situation where the data contains not only continuous variables but also discrete variables such as binary and count values. We also propose approximate Bayesian inference for parameters defined by loss functions based on posterior predictive distributing of missing observations, by extending bootstrap-based Bayesian inference for complete data. The proposed method is demonstrated through numerical studies using simulated and real data.

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arXiv2022

Grouped Generalized Estimating Equations for Longitudinal Data Analysis

Generalized estimating equation (GEE) is widely adopted for regression modeling for longitudinal data, taking account of potential correlations within the same subjects. Although the standard GEE assumes common regression coefficients among all the subjects, such an assumption may not be realistic when there is potential heterogeneity in regression coefficients among subjects. In this paper, we develop a flexible and interpretable approach, called grouped GEE analysis, to modeling longitudinal data with allowing heterogeneity in regression coefficients. The proposed method assumes that the subjects are divided into a finite number of groups and subjects within the same group share the same regression coefficient. We provide a simple algorithm for grouping subjects and estimating the regression coefficients simultaneously, and show the asymptotic properties of the proposed estimator. The number of groups can be determined by the cross-validation with averaging method. We demonstrate the proposed method through simulation studies and an application to a real dataset.

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arXiv2022

Adaptation of the Tuning Parameter in General Bayesian Inference with Robust Divergence

We introduce a methodology for robust Bayesian estimation with robust divergence (e.g., density power divergence or γ-divergence), indexed by a single tuning parameter. It is well known that the posterior density induced by robust divergence gives highly robust estimators against outliers if the tuning parameter is appropriately and carefully chosen. In a Bayesian framework, one way to find the optimal tuning parameter would be using evidence (marginal likelihood). However, we numerically illustrate that evidence induced by the density power divergence does not work to select the optimal tuning parameter since robust divergence is not regarded as a statistical model. To overcome the problems, we treat the exponential of robust divergence as an unnormalized statistical model, and we estimate the tuning parameter via minimizing the Hyvarinen score. We also provide adaptive computational methods based on sequential Monte Carlo (SMC) samplers, which enables us to obtain the optimal tuning parameter and samples from posterior distributions simultaneously. The empirical performance of the proposed method through simulations and an application to real data are also provided.

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arXiv2022

Adaptively Robust Small Area Estimation: Balancing Robustness and Efficiency of Empirical Bayes Confidence Intervals

Empirical Bayes small area estimation based on the well-known Fay-Herriot model may produce unreliable estimates when outlying areas exist. Existing robust methods against outliers or model misspecification are generally inefficient when the assumed distribution is plausible. This paper proposes a simple modification of the standard empirical Bayes methods with adaptively balancing robustness and efficiency. The proposed method employs gamma-divergence instead of the marginal log-likelihood and optimizes a tuning parameter controlling robustness by pursuing the efficiency of empirical Bayes confidence intervals for areal parameters. We provide an asymptotic theory of the proposed method under both the correct specification of the assumed distribution and the existence of outlying areas. We investigate the numerical performance of the proposed method through simulations and an application to small area estimation of average crime numbers.

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arXiv2022

Robust Fitting of Mixture Models using Weighted Complete Estimating Equations

Mixture modeling, which considers the potential heterogeneity in data, is widely adopted for classification and clustering problems. Mixture models can be estimated using the Expectation-Maximization algorithm, which works with the complete estimating equations conditioned by the latent membership variables of the cluster assignment based on the hierarchical expression of mixture models. However, when the mixture components have light tails such as a normal distribution, the mixture model can be sensitive to outliers. This study proposes a method of weighted complete estimating equations (WCE) for the robust fitting of mixture models. Our WCE introduces weights to complete estimating equations such that the weights can automatically downweight the outliers. The weights are constructed similarly to the density power divergence for mixture models, but in our WCE, they depend only on the component distributions and not on the whole mixture. A novel expectation-estimating-equation (EEE) algorithm is also developed to solve the WCE. For illustrative purposes, a multivariate Gaussian mixture, a mixture of experts, and a multivariate skew normal mixture are considered, and how our EEE algorithm can be implemented for these specific models is described. The numerical performance of the proposed robust estimation method was examined using simulated and real datasets.

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arXiv2022

Trend Filtering for Functional Data

Despite increasing accessibility to function data, effective methods for flexibly estimating underlying functional trend are still scarce. We thereby develop functional version of trend filtering for estimating trend of functional data indexed by time or on general graph by extending the conventional trend filtering, a powerful nonparametric trend estimation technique, for scalar data. We formulate the new trend filtering by introducing penalty terms based on $L_2$-norm of the differences of adjacent trend functions. We develop an efficient iteration algorithm for optimizing the objective function obtained by orthonormal basis expansion. Furthermore, we introduce additional penalty terms to eliminate redundant basis functions, which leads to automatic adaptation of the number of basis functions. The tuning parameter in the proposed method is selected via cross validation. We demonstrate the proposed method through simulation studies and applications to real world datasets.

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arXiv2021

Adaptively Robust Geographically Weighted Regression

We develop a new robust geographically weighted regression method in the presence of outliers. We embed the standard geographically weighted regression in robust objective function based on $γ$-divergence. A novel feature of the proposed approach is that two tuning parameters that control robustness and spatial smoothness are automatically tuned in a data-dependent manner. Further, the proposed method can produce robust standard error estimates of the robust estimator and give us a reasonable quantity for local outlier detection. We demonstrate that the proposed method is superior to the existing robust version of geographically weighted regression through simulation and data analysis.

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arXiv2021

On Selection Criteria for the Tuning Parameter in Robust Divergence

While robust divergence such as density power divergence and $γ$-divergence is helpful for robust statistical inference in the presence of outliers, the tuning parameter that controls the degree of robustness is chosen in a rule-of-thumb, which may lead to an inefficient inference. We here propose a selection criterion based on an asymptotic approximation of the Hyvarinen score applied to an unnormalized model defined by robust divergence. The proposed selection criterion only requires first and second-order partial derivatives of an assumed density function with respect to observations, which can be easily computed regardless of the number of parameters. We demonstrate the usefulness of the proposed method via numerical studies using normal distributions and regularized linear regression.

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arXiv2021

General Unbiased Estimating Equations for Variance Components in Linear Mixed Models

This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator. We derive the asymptotic covariance matrices and second-order biases under general estimating equations without assuming the normality of the underlying distributions and identify a class of second-order unbiased estimators of variance components. It is also shown that the asymptotic covariance matrices and second-order biases do not depend on whether the regression coefficients are estimated by the generalized or ordinary least squares methods. We carry out numerical studies to check the performance of the proposed method based on typical linear mixed models.

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arXiv2021

Spatially Clustered Regression

Spatial regression or geographically weighted regression models have been widely adopted to capture the effects of auxiliary information on a response variable of interest over a region. In contrast, relationships between response and auxiliary variables are expected to exhibit complex spatial patterns in many applications. This paper proposes a new approach for spatial regression, called spatially clustered regression, to estimate possibly clustered spatial patterns of the relationships. We combine K-means-based clustering formulation and penalty function motivated from a spatial process known as Potts model for encouraging similar clustering in neighboring locations. We provide a simple iterative algorithm to fit the proposed method, scalable for large spatial datasets. Through simulation studies, the proposed method demonstrates its superior performance to existing methods even under the true structure does not admit spatial clustering. Finally, the proposed method is applied to crime event data in Tokyo and produces interpretable results for spatial patterns. The R code is available at https://github.com/sshonosuke/SCR.

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arXiv2021

Bayesian Semiparametric Modeling of Response Mechanism for Nonignorable Missing Data

Statistical inference with nonresponse is quite challenging, especially when the response mechanism is nonignorable. In this case, the validity of statistical inference depends on untestable correct specification of the response model. To avoid the misspecification, we propose semiparametric Bayesian estimation in which an outcome model is parametric, but the response model is semiparametric in that we do not assume any parametric form for the nonresponse variable. We adopt penalized spline methods to estimate the unknown function. We also consider a fully nonparametric approach to modeling the response mechanism by using radial basis function methods. Using Polya-gamma data augmentation, we developed an efficient posterior computation algorithm via Gibbs sampling in which most full conditional distributions can be obtained in familiar forms. The performance of the proposed method is demonstrated in simulation studies and an application to longitudinal data.

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