arXiv subjects

Shonosuke Sugasawa

Publications and source records attributed to Shonosuke Sugasawa.

At least 91 records · Page 5Linked to original sources

arXiv2021

Log-Regularly Varying Scale Mixture of Normals for Robust Regression

Linear regression with the classical normality assumption for the error distribution may lead to an undesirable posterior inference of regression coefficients due to the potential outliers. This paper considers the finite mixture of two components with thin and heavy tails as the error distribution, which has been routinely employed in applied statistics. For the heavily-tailed component, we introduce the novel class of distributions; their densities are log-regularly varying and have heavier tails than those of Cauchy distribution, yet they are expressed as a scale mixture of normal distributions and enable the efficient posterior inference by Gibbs sampler. We prove the robustness to outliers of the posterior distributions under the proposed models with a minimal set of assumptions, which justifies the use of shrinkage priors with unbounded densities for the coefficient vector in the presence of outliers. The extensive comparison with the existing methods via simulation study shows the improved performance of our model in point and interval estimation, as well as its computational efficiency. Further, we confirm the posterior robustness of our method in the empirical study with the shrinkage priors for regression coefficients.

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arXiv2020

On Global-local Shrinkage Priors for Count Data

Global-local shrinkage prior has been recognized as useful class of priors which can strongly shrink small signals towards prior means while keeping large signals unshrunk. Although such priors have been extensively discussed under Gaussian responses, we intensively encounter count responses in practice in which the previous knowledge of global-local shrinkage priors cannot be directly imported. In this paper, we discuss global-local shrinkage priors for analyzing sequence of counts. We provide sufficient conditions under which the posterior mean keeps the observation as it is for very large signals, known as tail robustness property. Then, we propose tractable priors to meet the derived conditions approximately or exactly and develop an efficient posterior computation algorithm for Bayesian inference. The proposed methods are free from tuning parameters, that is, all the hyperparameters are automatically estimated based on the data. We demonstrate the proposed methods through simulation and an application to a real dataset.

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arXiv2020

Parametric Bootstrap Confidence Intervals for the Multivariate Fay-Herriot Model

The multivariate Fay-Herriot model is quite effective in combining information through correlations among small area survey estimates of related variables or historical survey estimates of the same variable or both. Though the literature on small area estimation is already very rich, construction of second-order efficient confidence intervals from multivariate models have so far received very little attention. In this paper, we develop a parametric bootstrap method for constructing a second-order efficient confidence interval for a general linear combination of small area means using the multivariate Fay-Herriot normal model. The proposed parametric bootstrap method replaces difficult and tedious analytical derivations by the power of efficient algorithm and high speed computer. Moreover, the proposed method is more versatile than the analytical method because the parametric bootstrap method can be easily applied to any method of model parameter estimation and any specific structure of the variance-covariance matrix of the multivariate Fay-Herriot model avoiding all the cumbersome and time-consuming calculations required in the analytical method. We apply our proposed methodology in constructing confidence intervals for the median income of four-person families for the fifty states and the District of Columbia in the United States. Our data analysis demonstrates that the proposed parametric bootstrap method generally provides much shorter confidence intervals compared to the corresponding traditional direct method. Moreover, the confidence intervals obtained from the multivariate model is generally shorter than the corresponding univariate model indicating the potential advantage of exploiting correlations of median income of four-person families with median incomes of three and five person families.

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arXiv2020

Improved Confidence Regions in Meta-analysis of Diagnostic Test Accuracy

Meta-analyses of diagnostic test accuracy (DTA) studies have been gathering attention in research in clinical epidemiology and health technology development, and bivariate random-effects model is becoming a standard tool. However, standard inference methods usually underestimate statistical errors and possibly provide highly overconfident results under realistic situations since they ignore the variability in the estimation of variance parameters. To overcome the difficulty, a new improved inference method, namely, an accurate confidence region for the meta-analysis of DTA, by asymptotically expanding the coverage probability of the standard confidence region. The advantage of the proposed confidence region is that it holds a relatively simple expression and does not require any repeated calculations such as Bootstrap or Monte Carlo methods to compute the region, thereby the proposed method can be easily carried out in practical applications. The effectiveness of the proposed method is demonstrated through simulation studies and an application to meta-analysis of screening test accuracy for alcohol problems.

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arXiv2020

Robust Bayesian Regression with Synthetic Posterior

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not necessarily straightforward. We here propose a Bayesian approach to robust inference on linear regression models using synthetic posterior distributions based on $γ$-divergence, which enables us to naturally assess the uncertainty of the estimation through the posterior distribution. We also consider the use of shrinkage priors for the regression coefficients to carry out robust Bayesian variable selection and estimation simultaneously. We develop an efficient posterior computation algorithm by adopting the Bayesian bootstrap within Gibbs sampling. The performance of the proposed method is illustrated through simulation studies and applications to famous datasets.

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arXiv2020

Predicting Infection of COVID-19 in Japan: State Space Modeling Approach

The number of confirmed cases of the coronavirus disease (COVID-19) in Japan has been increasing day by day and has had a serious impact on the society especially after the declaration of the state of emergency on April 7, 2020. This study analyzes the real time data from March 1 to April 22, 2020 by adopting a sophisticated statistical modeling tool based on the state space model combined with the well-known susceptible-exposed-infected (SIR) model. The model estimation and forecasting are conducted using the Bayesian methodology. The present study provides the parameter estimates of the unknown parameters that critically determine the epidemic process derived from the SIR model and prediction of the future transition of the infectious proportion including the size and timing of the epidemic peak with the prediction intervals that naturally accounts for the uncertainty. The prediction results under various scenarios reveals that the temporary reduction in the infection rate until the planned lifting of the state on May 6 will only delay the epidemic peak slightly. In order to minimize the spread of the epidemic, it is strongly suggested that an intervention is carried out for an extended period of time and that the government and individuals make a long term effort to reduce the infection rate even after the lifting.

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arXiv2020

An Approximate Bayesian Approach to Model-assisted Survey Estimation with Many Auxiliary Variables

Model-assisted estimation with complex survey data is an important practical problem in survey sampling. When there are many auxiliary variables, selecting significant variables associated with the study variable would be necessary to achieve efficient estimation of population parameters of interest. In this paper, we formulate a regularized regression estimator in the framework of Bayesian inference using the penalty function as the shrinkage prior for model selection. The proposed Bayesian approach enables us to get not only efficient point estimates but also reasonable credible intervals. Results from two limited simulation studies are presented to facilitate comparison with existing frequentist methods.

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arXiv2020

Efficient testing and effect size estimation for set-based genetic association inference via semiparametric multilevel mixture modeling: Application to a genome-wide association study of coronary artery disease

In genetic association studies, rare variants with extremely small allele frequency play a crucial role in complex traits, and the set-based testing methods that jointly assess the effects of groups of single nucleotide polymorphisms (SNPs) were developed to improve powers for the association tests. However, the powers of these tests are still severely limited due to the extremely small allele frequency, and precise estimations for the effect sizes of individual SNPs are substantially impossible. In this article, we provide an efficient set-based inference framework that addresses the two important issues simultaneously based on a Bayesian semiparametric multilevel mixture model. We propose to use the multilevel hierarchical model that incorporate the variations in set-specific effects and variant-specific effects, and to apply the optimal discovery procedure (ODP) that achieves the largest overall power in multiple significance testing. In addition, we provide Bayesian optimal "set-based" estimator of the empirical distribution of effect sizes. Efficiency of the proposed methods is demonstrated through application to a genome-wide association study of coronary artery disease (CAD), and through simulation studies. These results suggested there could be a lot of rare variants with large effect sizes for CAD, and the number of significant sets detected by the ODP was much greater than those by existing methods.

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arXiv2020

Grouped Heterogeneous Mixture Modeling for Clustered Data

Clustered data is ubiquitous in a variety of scientific fields. In this paper, we propose a flexible and interpretable modeling approach, called grouped heterogenous mixture modeling, for clustered data, which models cluster-wise conditional distributions by mixtures of latent conditional distributions common to all the clusters. In the model, we assume that clusters are divided into a finite number of groups and mixing proportions are the same within the same group. We provide a simple generalized EM algorithm for computing the maximum likelihood estimator, and an information criterion to select the numbers of groups and latent distributions. We also propose structured grouping strategies by introducing penalties on grouping parameters in the likelihood function. Under the settings where both the number of clusters and cluster sizes tend to infinity, we present asymptotic properties of the maximum likelihood estimator and the information criterion. We demonstrate the proposed method through simulation studies and an application to crime risk modeling in Tokyo.

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arXiv2020

Shrinkage with Robustness: Log-Adjusted Priors for Sparse Signals

We introduce a new class of distributions named log-adjusted shrinkage priors for the analysis of sparse signals, which extends the three parameter beta priors by multiplying an additional log-term to their densities. The proposed prior has density tails that are heavier than even those of the Cauchy distribution and realizes the tail-robustness of the Bayes estimator, while keeping the strong shrinkage effect on noises. We verify this property via the improved posterior mean squared errors in the tail. An integral representation with latent variables for the new density is available and enables fast and simple Gibbs samplers for the full posterior analysis. Our log-adjusted prior is significantly different from existing shrinkage priors with logarithms for allowing its further generalization by multiple log-terms in the density. The performance of the proposed priors is investigated through simulation studies and data analysis.

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arXiv2020

Efficient screening of predictive biomarkers for individual treatment selection

The development of molecular diagnostic tools to achieve individualized medicine requires identifying predictive biomarkers associated with subgroups of individuals who might receive beneficial or harmful effects from different available treatments. However, due to the large number of candidate biomarkers in the large-scale genetic and molecular studies, and complex relationships among clinical outcome, biomarkers and treatments, the ordinary statistical tests for the interactions between treatments and covariates have difficulties from their limited statistical powers. In this paper, we propose an efficient method for detecting predictive biomarkers. We employ weighted loss functions of Chen et al. (2017) to directly estimate individual treatment scores and propose synthetic posterior inference for effect sizes of biomarkers. We develop an empirical Bayes approach, namely, we estimate unknown hyperparameters in the prior distribution based on data. We then provide efficient screening methods for the candidate biomarkers via optimal discovery procedure with adequate control of false discovery rate. The proposed method is demonstrated in simulation studies and an application to a breast cancer clinical study in which the proposed method was shown to detect the much larger numbers of significant biomarkers than existing standard methods.

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arXiv2020

Small Area Estimation with Spatially Varying Natural Exponential Families

Two-stage hierarchical models have been widely used in small area estimation to produce indirect estimates of areal means. When the areas are treated exchangeably and the model parameters are assumed to be the same over all areas, we might lose the efficiency in the presence of spatial heterogeneity. To overcome this problem, we consider a two-stage area-level model based on natural exponential family with spatially varying model parameters. We employ geographically weighted regression approach to estimating the varying parameters and suggest a new empirical Bayes estimator of the areal mean. We also discuss some related problems, including the mean squared error estimation, benchmarked estimation, and estimation in non-sampled areas. The performance of the proposed method is evaluated through simulations and applications to two data sets.

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arXiv2019

Robust Empirical Bayes Small Area Estimation with Density Power Divergence

A two-stage normal hierarchical model called the Fay--Herriot model and the empirical Bayes estimator are widely used to provide indirect and model-based estimates of means in small areas. However, the performance of the empirical Bayes estimator might be poor when the assumed normal distribution is misspecified. In this article, we propose a simple modification by using density power divergence and suggest a new robust empirical Bayes small area estimator. The mean squared error and estimated mean squared error of the proposed estimator are derived based on the asymptotic properties of the robust estimator of the model parameters. We investigate the numerical performance of the proposed method through simulations and an application to survey data.

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arXiv2019

Bayesian approach to Lorenz curve using time series grouped data

This study is concerned with estimating the inequality measures associated with the underlying hypothetical income distribution from the times series grouped data on the Lorenz curve. We adopt the Dirichlet pseudo likelihood approach where the parameters of the Dirichlet likelihood are set to the differences between the Lorenz curve of the hypothetical income distribution for the consecutive income classes and propose a state space model which combines the transformed parameters of the Lorenz curve through a time series structure. Furthermore, the information on the sample size in each survey is introduced into the originally nuisance Dirichlet precision parameter to take into account the variability from the sampling. From the simulated data and real data on the Japanese monthly income survey, it is confirmed that the proposed model produces more efficient estimates on the inequality measures than the existing models without time series structures.

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arXiv2019

Estimation and inference for area-wise spatial income distributions from grouped data

Estimating income distributions plays an important role in the measurement of inequality and poverty over space. The existing literature on income distributions predominantly focuses on estimating an income distribution for a country or a region separately and the simultaneous estimation of multiple income distributions has not been discussed in spite of its practical importance. In this work, we develop an effective method for the simultaneous estimation and inference for area-wise spatial income distributions taking account of geographical information from grouped data. Based on the multinomial likelihood function for grouped data, we propose a spatial state-space model for area-wise parameters of parametric income distributions. We provide an efficient Bayesian approach to estimation and inference for area-wise latent parameters, which enables us to compute area-wise summary measures of income distributions such as mean incomes and Gini indices, not only for sampled areas but also for areas without any samples thanks to the latent spatial state-space structure. The proposed method is demonstrated using the Japanese municipality-wise grouped income data. The simulation studies show the superiority of the proposed method to a crude conventional approach which estimates the income distributions separately.

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arXiv2019

A Unified Method for Improved Inference in Random-effects Meta-analysis

Random-effects meta-analyses have been widely applied in evidence synthesis for various types of medical studies. However, standard inference methods (e.g. restricted maximum likelihood estimation) usually underestimate statistical errors and possibly provide highly overconfident results under realistic situations; for instance, coverage probabilities of confidence intervals can be substantially below the nominal level. The main reason is that these inference methods rely on large sample approximations even though the number of synthesized studies is usually small or moderate in practice. In this article we solve this problem using a unified inference method based on Monte Carlo conditioning for broad application to random-effects meta-analysis. The developed method provides improved confidence intervals with coverage probabilities that are closer to the nominal level than standard methods. As specific applications, we provide new inference procedures for three types of meta-analysis: conventional univariate meta-analysis for pairwise treatment comparisons, meta-analysis of diagnostic test accuracy, and multiple treatment comparisons via network meta-analysis. We also illustrate the practical effectiveness of these methods via real data applications and simulation studies.

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arXiv2018

Adaptively Transformed Mixed Model Prediction of General Finite Population Parameters

For estimating area-specific parameters (quantities) in a finite population, a mixed model prediction approach is attractive. However, this approach strongly depends on the normality assumption of the response values although we often encounter a non-normal case in practice. In such a case, transforming observations to make them suitable for normality assumption is a useful tool, but the problem of selecting suitable transformation still remains open. To overcome the difficulty, we here propose a new empirical best predicting method by using a parametric family of transformations to estimate a suitable transformation based on the data. We suggest a simple estimating method for transformation parameters based on the profile likelihood function, which achieves consistency under some conditions on transformation functions. For measuring variability of point prediction, we construct an empirical Bayes confidence interval of the population parameter of interest. Through simulation studies, we investigate numerical performance of the proposed methods. Finally, we apply the proposed method to synthetic income data in Spanish provinces in which the resulting estimates indicate that the commonly used log-transformation would not be appropriate.

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arXiv2018

Estimation and Prediction in Transformed Nested Error Regression Models

This paper suggests parametrically transformed nested error regression models (TNERM), which transform the data flexibly to follow the normal linear mixed regression. We provide a procedure for estimating consistently the parameters of the proposed model and a predictor based on the consistent estimators. Then, in order to calibrate uncertainty of the transformed empirical best linear unbiased predictor, we derive prediction intervals with second-order accuracy based on the parametric bootstrap method. The proposed methods are investigated through simulation and empirical studies.

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